Question 1

In an arithmetic progression, the sum of the first 10 terms is 155, and the first term is 5. What is the common difference?

Accepted Answer

Correct Option: A. Solution: The sum of the first n terms of an AP is given by $S_n = \frac{n}{2} (2a + (n - 1)d)$. Substituting the given values, $155 = \frac{10}{2} (2 	imes 5 + 9d)$. Solving for $d$, we get $d = 3$.

Question 2

The sum of the first 20 terms of an arithmetic progression is 210. If the first term is 3, what is the common difference?

Accepted Answer

Correct Option: A. Solution: The sum of the first n terms of an AP is given by $S_n = \frac{n}{2} \cdot (2a + (n-1)d)$. For $S_{20} = 210$, $\frac{20}{2} \cdot (2 \cdot 3 + 19d) = 210$. Solving gives $d = 0.5$.

Question 3

Reena's salary follows an arithmetic progression. If her starting salary is ₹8000 with an annual increment of ₹500, in which year will her salary be ₹11000?

Accepted Answer

Correct Option: C. Solution: The salary in the nth year is given by the formula $a_n = a + (n-1)d$, where $a = 8000$ and $d = 500$. Setting $a_n = 11000$, we solve $11000 = 8000 + (n-1)500$. Simplifying, $n = 7$. Therefore, her salary will be ₹11000 in the 7th year.

Question 4

Given an arithmetic progression with first term $a = 5$ and common difference $d = 6$, which term is $301$?

Accepted Answer

Correct Option: B. Solution: Using the formula for the nth term of an AP, $a_n = a + (n-1)d$, we have $301 = 5 + (n-1) 	imes 6$. Solving for $n$, we get $n = 51$. Therefore, the 51st term is $301$.

Question 5

Which of the following sequences is an arithmetic progression (AP)?

Accepted Answer

Correct Option: B. Solution: The sequence 2, 5, 8, 11, ... has a constant difference of 3 between consecutive terms, thus it forms an AP.

Question 6

Which term of the arithmetic progression 21, 18, 15, ... is -81?

Accepted Answer

Correct Option: B. Solution: Using $a_n = a + (n-1)d$, where $a = 21$, $d = -3$, and $a_n = -81$: $-81 = 21 + (n-1)(-3)$. Solving gives $n = 35$.

Question 7

Find the sum of the first 10 terms of the arithmetic progression: 2, 7, 12, ...

Accepted Answer

Correct Option: C. Solution: The sum of the first $n$ terms of an AP is $S_n = \frac{n}{2} [2a + (n-1)d]$. Here, $a = 2$, $d = 5$, and $n = 10$. So, $S_{10} = \frac{10}{2} [2 	imes 2 + (10-1) 	imes 5] = 250$.

Question 8

Which term of the AP: 121, 117, 113, ... is the first negative term?

Accepted Answer

Correct Option: B. Solution: The nth term is given by $a_n = 121 + (n - 1)(-4)$. Setting $a_n < 0$, we solve $121 - 4n + 4 < 0$, giving $n > 31.25$. Thus, the 32nd term is the first negative term.

Question 9

If the first term $a$ of an AP is 5 and the common difference $d$ is 3, what is the sum of the first 10 terms?

Accepted Answer

Correct Option: A. Solution: Using the formula $S_n = \frac{n}{2} [2a + (n - 1) d]$, we get $S_{10} = \frac{10}{2} [2(5) + (10 - 1) 	imes 3] = 5 	imes [10 + 27] = 5 	imes 37 = 185$.

Question 10

Reena's starting monthly salary is ₹8000 with an annual increment of ₹500. What will be her monthly salary in the 10th year?

Accepted Answer

Correct Option: B. Solution: The salary for the nth year is given by $a_n = a + (n-1) 	imes d$. Here, $a = 8000$, $d = 500$, and $n = 10$. So, $a_{10} = 8000 + (10-1) 	imes 500 = 8000 + 4500 = 12500$.

Question 11

A ladder has rungs decreasing uniformly by 2 cm from bottom to top, with the bottom rung being 45 cm. What is the length of the 5th rung?

Accepted Answer

Correct Option: A. Solution: The length of the nth rung is given by $a_n = a + (n-1) 	imes d$. Here, $a = 45$, $d = -2$, and $n = 5$. So, $a_5 = 45 + (5-1) 	imes (-2) = 45 - 8 = 37$ cm.

Question 12

If the sum of the first 16 terms of an arithmetic progression is 400, and the first term is 10, what is the common difference?

Accepted Answer

Correct Option: B. Solution: The sum of the first n terms of an AP is given by $S_n = \frac{n}{2} (2a + (n - 1)d)$. Substituting the given values, $400 = \frac{16}{2} (2 	imes 10 + 15d)$. Solving for $d$, we get $d = 2$.

Question 13

Which term of the arithmetic progression 15, 12, 9, ... is the first negative term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is given by $a_n = a + (n - 1)d$. Here, $a = 15$, $d = -3$. We need to find $n$ such that $a_n < 0$. Solving $15 + (n - 1)(-3) < 0$, we get $n = 11$.

Question 14

Consider an arithmetic progression where the first term is $a = 5$ and the common difference is $d = 3$. What is the 20th term of this arithmetic progression?

Accepted Answer

Correct Option: A. Solution: The nth term of an AP is given by $a_n = a + (n - 1)d$. Substituting the given values, $a_{20} = 5 + (20 - 1) 	imes 3 = 5 + 57 = 62$.

Question 15

What is the formula for the nth term of an arithmetic progression (AP)?

Accepted Answer

Correct Option: A. Solution: The nth term of an AP is given by $a_n = a + (n - 1) \cdot d$, where $a$ is the first term and $d$ is the common difference.

Question 16

Consider an arithmetic progression where the first term is $a = 12$ and the common difference $d = 3$. If the sum of the first $n$ terms is 636, how many terms are there in this arithmetic progression?

Accepted Answer

Correct Option: B. Solution: The sum of the first $n$ terms of an AP is given by $S_n = \frac{n}{2} 	imes (2a + (n-1)d)$. Substituting $S_n = 636$, $a = 12$, and $d = 3$, we get $636 = \frac{n}{2} 	imes (24 + 3(n-1))$. Solving this equation, we find $n = 20$.

Question 17

Find the number of terms in the arithmetic progression: 9, 17, 25, ... if the sum of the terms is 636.

Accepted Answer

Correct Option: C. Solution: The sum of the first $n$ terms of an AP is $S_n = \frac{n}{2} 	imes (2a + (n-1)d)$. Here, $a = 9$, $d = 8$, and $S_n = 636$. Solving $636 = \frac{n}{2} 	imes (18 + 8(n-1))$ yields $n = 14$.

Question 18

What is the common difference in the arithmetic progression: 3, 8, 13, 18, ...?

Accepted Answer

Correct Option: B. Solution: The common difference $d$ is obtained by subtracting any term from the succeeding term. Here, $d = 8 - 3 = 5$.

Question 19

In an arithmetic progression, the sum of the first 20 terms is 2100 and the first term is 10. What is the common difference?

Accepted Answer

Correct Option: A. Solution: The sum of the first n terms of an AP is given by $S_n = \frac{n}{2} \cdot (2a + (n - 1) \cdot d)$. Here, $S_{20} = 2100$, $a = 10$, and $n = 20$. So, $2100 = \frac{20}{2} \cdot (2 \cdot 10 + 19 \cdot d)$. Solving, $2100 = 10 \cdot (20 + 19d)$, $210 = 20 + 19d$, $190 = 19d$, $d = 10$.

Question 20

A ladder has rungs that decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If there are 11 rungs, what is the length of the 6th rung?

Accepted Answer

Correct Option: B. Solution: The sequence of rung lengths is an arithmetic progression (AP) with first term $a = 45$ cm and common difference $d = -2$ cm. The nth term is given by $a_n = a + (n - 1) \cdot d$. For the 6th rung, $a_6 = 45 + (6 - 1) \cdot (-2) = 45 - 10 = 35$ cm.

Question 21

A ladder has rungs 25 cm apart. The length of the rungs decreases uniformly from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 m apart, how many rungs are there?

Accepted Answer

Correct Option: B. Solution: The distance between the top and bottom rungs is 2.5 m or 250 cm. Since the rungs are 25 cm apart, the number of gaps between the rungs is $\frac{250}{25} = 10$. Therefore, the number of rungs is 11.

Question 22

In an arithmetic progression (AP) with first term $a = 21$ and common difference $d = -3$, which term is $-81$?

Accepted Answer

Correct Option: B. Solution: Using the formula for the nth term of an AP, $a_n = a + (n-1)d$, we have $-81 = 21 + (n-1)(-3)$. Solving for $n$, we get $n = 35$. Therefore, the 35th term is $-81$.

Question 23

Consider an arithmetic progression where the first term is $a = 5$ and the common difference is $d = 3$. What is the sum of the first 10 terms?

Accepted Answer

Correct Option: C. Solution: The sum of the first $n$ terms of an AP is given by $S_n = \frac{n}{2} [2a + (n-1)d]$. Substituting $n = 10$, $a = 5$, and $d = 3$, we get $S_{10} = \frac{10}{2} [2 	imes 5 + (10-1) 	imes 3] = 5 [10 + 27] = 5 	imes 37 = 185$.

Question 24

Which term of the arithmetic progression: 121, 117, 113, ... is the first negative term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is $a_n = a + (n-1) \cdot d$. Here, $a = 121$, $d = -4$. Setting $a_n < 0$, we solve $121 + (n-1)(-4) < 0$ to find $n = 32$.

Question 25

In an arithmetic progression (AP), if the first term is $a = 5$ and the common difference is $d = 3$, what is the 10th term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is given by $a_n = a + (n-1) \cdot d$. Substituting $a = 5$, $d = 3$, and $n = 10$, we get $a_{10} = 5 + (10-1) \cdot 3 = 5 + 27 = 32$.

Question 26

If the 5th term of an arithmetic progression is 20 and the 10th term is 35, what is the common difference?

Accepted Answer

Correct Option: A. Solution: The nth term of an AP is given by $a_n = a + (n-1)d$. For the 5th term, $a_5 = a + 4d = 20$, and for the 10th term, $a_{10} = a + 9d = 35$. Subtracting these equations gives $5d = 15$, so $d = 3$.

Question 27

In a savings scheme, the amount becomes 4 times of itself after every 3 years. What will be the maturity amount of an investment of ₹8000 after 9 years?

Accepted Answer

Correct Option: B. Solution: The maturity amount after 9 years is the third term in the sequence: 10000, 12500, 15625, 19531.25. Hence, the maturity amount is ₹15625.

Question 28

A ladder has rungs that decrease uniformly by 2 cm from bottom to top, with the bottom rung being 45 cm. How long is the 10th rung?

Accepted Answer

Correct Option: A. Solution: The length of the nth rung is given by $a_n = a + (n - 1) 	imes d$, where $a = 45$ cm and $d = -2$ cm. For the 10th rung, $a_{10} = 45 + (10 - 1) 	imes (-2) = 45 - 18 = 27$ cm.

Question 29

If the sum of the third and seventh terms of an AP is 6 and their product is 8, what is the first term of the AP?

Accepted Answer

Correct Option: A. Solution: Let the first term be $a$ and the common difference be $d$. The third term is $a_3 = a + 2d$ and the seventh term is $a_7 = a + 6d$. Given $a_3 + a_7 = 6$, we have $2a + 8d = 6$. Also, $a_3 	imes a_7 = 8$, giving $(a + 2d)(a + 6d) = 8$. Solving these equations, we find $a = 1$ and $d = 1$.

Question 30

Shakila puts ₹100 into her daughter's money box at age one and increases the amount by ₹50 each year. How much money will be in the box on her daughter's 21st birthday?

Accepted Answer

Correct Option: C. Solution: The amount on the 21st birthday is the sum of the first 21 terms of the AP where $a = 100$ and $d = 50$. The sum $S_n = \frac{n}{2} [2a + (n - 1)d]$. So, $S_{21} = \frac{21}{2} [2 	imes 100 + 20 	imes 50] = \frac{21}{2} 	imes 1200 = 12,600$.

Question 31

In an arithmetic progression, the first term is 5 and the last term is 45. If the sum of all terms is 400, what is the common difference?

Accepted Answer

Correct Option: A. Solution: The sum of an AP is given by $S_n = \frac{n}{2} 	imes (a + l)$, where $a$ is the first term, $l$ is the last term, and $n$ is the number of terms. Here, $S_n = 400$, $a = 5$, and $l = 45$. Solving $400 = \frac{n}{2} 	imes (5 + 45)$ gives $n = 16$. The common difference $d = \frac{l - a}{n-1} = \frac{45 - 5}{15} = 2$.

Question 32

In an AP, the first term is 10 and the common difference is 5. Which of the following is the sum of the first 20 terms?

Accepted Answer

Correct Option: B. Solution: Using the formula $S_n = \frac{n}{2} [2a + (n - 1) d]$, we calculate $S_{20} = \frac{20}{2} [2(10) + (20 - 1) 	imes 5] = 10 	imes [20 + 95] = 10 	imes 115 = 1150$.

Question 33

The sum of the first 50 terms of an arithmetic progression is 1275. If the first term is 5, what is the common difference?

Accepted Answer

Correct Option: B. Solution: Using $S_n = \frac{n}{2} [2a + (n-1)d]$, with $S_{50} = 1275$, $a = 5$, and $n = 50$, we have $1275 = \frac{50}{2} [2 	imes 5 + 49d]$. Simplifying, $1275 = 25 [10 + 49d]$, leads to $10 + 49d = 51$, so $49d = 41$, giving $d = 1$.

Question 34

If the 5th term of an arithmetic progression is 20 and the 10th term is 35, what is the first term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is given by $a_n = a + (n-1) \cdot d$. For the 5th term, $a + 4d = 20$ and for the 10th term, $a + 9d = 35$. Solving these equations gives $a = 10$.

Question 35

What is the formula for the sum of the first $n$ terms of an arithmetic progression (AP)?

Accepted Answer

Correct Option: A. Solution: The sum of the first $n$ terms of an AP is given by $S_n = \frac{n}{2} [2a + (n - 1) d]$.

Question 36

In the arithmetic progression where the first term is 24 and the common difference is -3, which term is the first negative term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is given by $a_n = a + (n-1)d$. Here, $a = 24$ and $d = -3$. We need to find $n$ such that $a_n < 0$. Solving $24 + (n-1)(-3) < 0$, we get $n = 10$. Thus, the 10th term is the first negative term.

Question 37

Reena has a starting monthly salary of ₹8000 with an annual increment of ₹500. What will be her monthly salary in the 10th year?

Accepted Answer

Correct Option: B. Solution: The salary in the nth year is given by the formula $a_n = a + (n - 1) 	imes d$, where $a = 8000$ and $d = 500$. For the 10th year, $a_{10} = 8000 + (10 - 1) 	imes 500 = 8000 + 4500 = 13,000$.

Question 38

How many terms are there in the arithmetic progression: 9, 17, 25, ..., if the sum of the terms is 636?

Accepted Answer

Correct Option: C. Solution: The sum of the first $n$ terms of an AP is $S_n = \frac{n}{2} (2a + (n-1)d)$. Here, $a = 9$, $d = 8$, and $S_n = 636$. Solving $636 = \frac{n}{2} (2 \cdot 9 + (n-1) \cdot 8)$ gives $n = 14$.

Question 39

Given the sequence 3, 8, 13, 18, ..., which term is equal to 78?

Accepted Answer

Correct Option: B. Solution: The common difference $d = 8 - 3 = 5$. Using the formula $a_n = a + (n - 1) 	imes d$, we find $78 = 3 + (n - 1) 	imes 5$. Solving gives $n = 16$.

Question 40

If the first term of an arithmetic progression is 10 and the common difference is 3, what is the 5th term?

Accepted Answer

Correct Option: B. Solution: The nth term of an AP is given by $a_n = a + (n-1)d$. For the 5th term, $a_5 = 10 + (5-1) 	imes 3 = 22$.

Question 41

Consider the sequence: 5, 10, 15, 20, ... If the sequence continues, what will be the 50th term?

Accepted Answer

Correct Option: A. Solution: The sequence is an arithmetic progression (AP) with first term $a = 5$ and common difference $d = 5$. The nth term of an AP is given by $a_n = a + (n - 1) \cdot d$. Therefore, the 50th term is $a_{50} = 5 + (50 - 1) \cdot 5 = 5 + 245 = 250$.

Question 42

In an arithmetic progression, the sum of the first 16 terms is 400 and the common difference is 2. What is the first term?

Accepted Answer

Correct Option: B. Solution: Using the formula $S_n = \frac{n}{2} [2a + (n-1)d]$, and given $S_{16} = 400$, $d = 2$, and $n = 16$, we solve for $a$: $400 = \frac{16}{2} [2a + 15 	imes 2]$. Simplifying gives $400 = 8 [2a + 30]$, which leads to $2a + 30 = 50$, hence $2a = 20$, so $a = 10$.

Question 43

If the first term of an AP is 5 and the common difference is 3, what is the 10th term?

Accepted Answer

Correct Option: C. Solution: Using the formula $a_n = a + (n - 1) \cdot d$, we have $a_{10} = 5 + (10 - 1) \cdot 3 = 5 + 27 = 32$.

Question 44

If the first term $a$ of an arithmetic progression is 5 and the common difference $d$ is 3, then the sum of the first 10 terms is 95.

Accepted Answer

Answer: False. Solution: Using the formula $S_n = \frac{n}{2} [2a + (n - 1) d]$, we find $S_{10} = \frac{10}{2} [2 	imes 5 + (10 - 1) 	imes 3] = 5 	imes [10 + 27] = 5 	imes 37 = 185$. Therefore, the sum is 185, not 95.

Question 45

In an arithmetic progression (AP), the common difference can be zero.

Accepted Answer

Answer: True. Solution: An arithmetic progression can have a common difference of zero, resulting in all terms being the same.

Question 46

The nth term of an arithmetic progression (AP) is given by the formula $a_n = a + (n - 1) d$, where $a$ is the first term and $d$ is the common difference.

Accepted Answer

Answer: True. Solution: The formula $a_n = a + (n - 1) d$ is used to calculate the nth term of an AP, where $a$ is the first term and $d$ is the common difference.

Question 47

In an arithmetic progression, knowing only the first term is sufficient to determine the entire sequence.

Accepted Answer

Answer: False. Solution: To determine an arithmetic progression, both the first term and the common difference are required.

Question 48

In an arithmetic progression, each term is obtained by adding a fixed number to the preceding term.

Accepted Answer

Answer: True. Solution: An arithmetic progression (AP) is defined as a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term.

Question 49

The sequence 1, 1, 2, 3, 5, 8 is an arithmetic progression.

Accepted Answer

Answer: False. Solution: The sequence 1, 1, 2, 3, 5, 8 does not have a constant difference between consecutive terms, so it is not an arithmetic progression.

Question 50

If the first term of an arithmetic progression is 6 and the common difference is -3, the sequence will eventually include negative numbers.

Accepted Answer

Answer: True. Solution: Starting from 6 and repeatedly subtracting 3 will result in negative numbers, as the sequence progresses through positive, zero, and then negative values.

Question 51

In an arithmetic progression, the sum of the first $n$ terms can also be expressed as $S_n = \frac{n}{2} (a + l)$, where $l$ is the last term.

Accepted Answer

Answer: True. Solution: The formula $S_n = \frac{n}{2} (a + l)$ is applicable when the last term $l$ of the AP is known, as per the excerpt.

Question 52

The sequence of numbers representing the amount of money Reena receives as salary over the years forms a geometric progression.

Accepted Answer

Answer: False. Solution: Reena's salary increases by a fixed amount each year, forming an arithmetic progression, not a geometric progression.

Question 53

The formula $S_n = \frac{n}{2} [2a + (n - 1) d]$ for the sum of the first $n$ terms of an AP is only valid if the common difference $d$ is positive.

Accepted Answer

Answer: False. Solution: The formula $S_n = \frac{n}{2} [2a + (n - 1) d]$ is valid for any common difference $d$, whether positive, negative, or zero.

Question 54

In an arithmetic progression (AP), the nth term is given by the formula $a_n = a + (n - 1) \, d$, where $a$ is the first term and $d$ is the common difference.

Accepted Answer

Answer: True. Solution: The formula for the nth term of an AP is derived from the definition of an arithmetic progression, where each term is obtained by adding the common difference to the previous term.

Question 55

The sequence 1, 1, 2, 3, 5, 8 is an arithmetic progression.

Accepted Answer

Answer: False. Solution: The sequence 1, 1, 2, 3, 5, 8 is not an arithmetic progression because the difference between consecutive terms is not constant.

Question 56

The nth term of an arithmetic progression is given by $a_n = a + (n - 1) d$, where $a$ is the first term and $d$ is the common difference.

Accepted Answer

Answer: True. Solution: The formula $a_n = a + (n - 1) d$ correctly represents the nth term of an arithmetic progression.

Question 57

The nth term of an arithmetic progression, given by $a_n = a + (n - 1) \cdot d$, where $a$ is the first term, $d$ is the common difference, and $n$ is the term number, can be used to determine any term in the sequence.

Accepted Answer

Answer: True. Solution: The formula $a_n = a + (n - 1) \cdot d$ is specifically designed to calculate the nth term of an arithmetic progression by using the first term $a$, the common difference $d$, and the term number $n$. This allows us to determine any term in the sequence.

Question 58

A sequence is considered an arithmetic progression (AP) if the difference between consecutive terms is constant.

Accepted Answer

Answer: True. Solution: An arithmetic progression is defined as a sequence where each term after the first is obtained by adding a constant difference to the preceding term.

Question 59

If the common difference $d$ of an arithmetic progression is zero, then all terms of the sequence are identical.

Accepted Answer

Answer: True. Solution: In an arithmetic progression, if the common difference $d$ is zero, each term is obtained by adding zero to the previous term. Therefore, all terms in the sequence will be identical to the first term.

Question 60

The sum of the first $n$ terms of an arithmetic progression (AP) can be calculated using the formula $S_n = \frac{n}{2} [2a + (n - 1) d]$ where $a$ is the first term and $d$ is the common difference.

Accepted Answer

Answer: True. Solution: The formula $S_n = \frac{n}{2} [2a + (n - 1) d]$ is used to calculate the sum of the first $n$ terms of an AP, as stated in the excerpt.

Question 61

To find the number of terms in an arithmetic progression, it is sufficient to know only the first term and the common difference.

Accepted Answer

Answer: False. Solution: To find the number of terms in an AP, you need to know the first term, the common difference, and either the last term or the sum of the terms.

Question 62

In an arithmetic progression, the nth term is given by the formula $a_n = a + (n - 1) d$, where $a$ is the first term and $d$ is the common difference.

Accepted Answer

Answer: True. Solution: The formula $a_n = a + (n - 1) d$ is used to calculate the nth term of an arithmetic progression, where $a$ is the first term and $d$ is the common difference.

Question 63

A sequence where each term is obtained by adding a fixed number to the preceding term is always an Arithmetic Progression.

Accepted Answer

Answer: True. Solution: An Arithmetic Progression (AP) is defined as a sequence where each term is obtained by adding a fixed number, known as the common difference, to the preceding term.

Question 64

The formula $S_n = \frac{n}{2} (a + l)$ for the sum of the first $n$ terms of an arithmetic progression can be used when the last term $l$ is known.

Accepted Answer

Answer: True. Solution: The formula $S_n = \frac{n}{2} (a + l)$ is applicable when the last term $l$ of the finite AP is known, allowing for an alternative calculation of the sum.

Arithmetic Progressions

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Arithmetic Progression (AP)

Nth Term of an AP

Sum of First n Terms of an AP

Determining AP Characteristics

Applications of AP in Real-Life Problems

Examples

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Arithmetic Progression (AP)

Nth Term of an AP

Sum of First n Terms of an AP

Determining AP Characteristics

Applications of AP in Real-Life Problems

General Exam Tips

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Multiple Choice Questions

Q1.In an arithmetic progression, the sum of the first 10 terms is 155, and the first term is 5. What is the common difference?

Correct Answer: A

Q2.The sum of the first 20 terms of an arithmetic progression is 210. If the first term is 3, what is the common difference?

Correct Answer: A

Q3.Reena's salary follows an arithmetic progression. If her starting salary is ₹8000 with an annual increment of ₹500, in which year will her salary be ₹11000?

Correct Answer: C

Q4.Given an arithmetic progression with first term a=5a = 5a=5 and common difference d=6d = 6d=6, which term is 301301301?

Correct Answer: B

Q5.Which of the following sequences is an arithmetic progression (AP)?

Correct Answer: B

Q6.Which term of the arithmetic progression 21, 18, 15, ... is -81?

Correct Answer: B

Q7.Find the sum of the first 10 terms of the arithmetic progression: 2, 7, 12, ...

Correct Answer: C

Q8.Which term of the AP: 121, 117, 113, ... is the first negative term?

Correct Answer: B

Q9.If the first term aaa of an AP is 5 and the common difference ddd is 3, what is the sum of the first 10 terms?

Correct Answer: A

Q10.Reena's starting monthly salary is ₹8000 with an annual increment of ₹500. What will be her monthly salary in the 10th year?

Correct Answer: B

Q11.A ladder has rungs decreasing uniformly by 2 cm from bottom to top, with the bottom rung being 45 cm. What is the length of the 5th rung?

Correct Answer: A

Q12.If the sum of the first 16 terms of an arithmetic progression is 400, and the first term is 10, what is the common difference?

Correct Answer: B

Q13.Which term of the arithmetic progression 15, 12, 9, ... is the first negative term?

Correct Answer: B

Q14.Consider an arithmetic progression where the first term is a=5a = 5a=5 and the common difference is d=3d = 3d=3. What is the 20th term of this arithmetic progression?

Correct Answer: A

Q15.What is the formula for the nth term of an arithmetic progression (AP)?

Correct Answer: A

Q16.Consider an arithmetic progression where the first term is a=12a = 12a=12 and the common difference d=3d = 3d=3. If the sum of the first nnn terms is 636, how many terms are there in this arithmetic progression?

Correct Answer: B

Q17.Find the number of terms in the arithmetic progression: 9, 17, 25, ... if the sum of the terms is 636.

Correct Answer: C

Q18.What is the common difference in the arithmetic progression: 3, 8, 13, 18, ...?

Correct Answer: B

Q19.In an arithmetic progression, the sum of the first 20 terms is 2100 and the first term is 10. What is the common difference?

Correct Answer: A

Q20.A ladder has rungs that decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If there are 11 rungs, what is the length of the 6th rung?

Correct Answer: B

Q21.A ladder has rungs 25 cm apart. The length of the rungs decreases uniformly from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 m apart, how many rungs are there?

Correct Answer: B

Q22.In an arithmetic progression (AP) with first term a=21a = 21a=21 and common difference d=−3d = -3d=−3, which term is −81-81−81?

Correct Answer: B

Q23.Consider an arithmetic progression where the first term is a=5a = 5a=5 and the common difference is d=3d = 3d=3. What is the sum of the first 10 terms?

Correct Answer: C

Q24.Which term of the arithmetic progression: 121, 117, 113, ... is the first negative term?

Correct Answer: B

Q25.In an arithmetic progression (AP), if the first term is a=5a = 5a=5 and the common difference is d=3d = 3d=3, what is the 10th term?

Correct Answer: B

Q26.If the 5th term of an arithmetic progression is 20 and the 10th term is 35, what is the common difference?

Correct Answer: A

Q27.In a savings scheme, the amount becomes 4 times of itself after every 3 years. What will be the maturity amount of an investment of ₹8000 after 9 years?