Arithmetic Progressions Practice Questions

Class 10 · Mathematics · 816 free MCQs with instant results and detailed explanations.

816

Total

271

Easy

376

Medium

169

Hard

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Topics in Arithmetic Progressions

Sum of n Terms 240

Applications of AP 305

nth Term of AP 271

Sample Questions from Arithmetic Progressions

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

In an arithmetic progression, if the first term is 8 and the common difference is -2, what is the 5th term?

A. 0

B. 2

C. 4

D. -2

Show Answer & Explanation

Correct Answer: A

Using Tn = a + (n-1)d, T5 = 8 + (5-1)(-2) = 8 - 8 = 0.

Easy

If the 7th term of an AP is 20 and the common difference is 4, what is the first term?

A. 12

B. 16

C. 8

D. 24

Show Answer & Explanation

Correct Answer: A

Using the formula Tn = a + (n-1)d, we have 20 = a + 6×4. Thus, a = 20 - 24 = -4.

Easy

In an AP, if the first term is 10 and the 4th term is 22, what is the common difference?

A. 3

B. 4

C. 5

D. 6

Show Answer & Explanation

Correct Answer: B

Using T4 = a + 3d, we have 22 = 10 + 3d, which gives 3d = 12, making d = 4.

Medium

In an arithmetic progression, if the sum of the first 5 terms is 75, what is the common difference if the first term is 15?

A. 3

B. 5

C. 6

D. 9

Show Answer & Explanation

Correct Answer: B

The sum of the first n terms of an AP is given by S_n = n/2 * (2a + (n-1)d). For 5 terms: S_5 = 5/2 * (2*15 + 4d) = 75. Solving gives d = 5.

Medium

If the first term of an AP is 8 and the last term is 80, with 20 terms, what is the common difference?

A. 4

B. 3.6

C. 4.5

D. 5

Show Answer & Explanation

Correct Answer: A

The nth term formula gives us a_n = a + (n-1)d. Here, a = 8, a_n = 80, n = 20. Thus, 80 = 8 + (20-1)d leads to d = (80 - 8)/19 = 72/19 = 4.

Medium

If the first term of an AP is 3 and the sum of the first 10 terms is 150, find the common difference.

A. 3

B. 5

C. 7

D. 9

Show Answer & Explanation

Correct Answer: B

Using the sum formula S_n = n/2 * (2a + (n-1)d), we can find the common difference. Here, 150 = 10/2 * (6 + 9d). Solving gives d = 5.

Medium

If the 5th term of an AP is 20 and the 12th term is 50, what is the common difference?

A. 10/7

B. 5

C. 30/7

D. 15/7

Show Answer & Explanation

Correct Answer: C

We can set up equations based on the nth term formula and find d from the difference between terms.

Hard

In an arithmetic progression, the 5th term is 20 and the 10th term is 35. What is the first term of the AP?

A. 5

B. 10

C. 15

D. 0

Show Answer & Explanation

Correct Answer: A

To find the first term, use the formula for the nth term: a_n = a + (n-1)d. Here, set up equations for the 5th and 10th terms to solve for 'a'.

Hard

If the nth term of an AP is given by 3n + 2, what is the 15th term?

A. 47

B. 45

C. 44

D. 49

Show Answer & Explanation

Correct Answer: A

Substituting n = 15 into the formula 3n + 2 gives the value of the 15th term directly.

Q10

Hard

The first term of an AP is -4, and the common difference is 3. What is the 12th term of the AP?

A. 29

B. 28

C. 30

D. 23

Show Answer & Explanation

Correct Answer: A

The nth term formula a_n = a + (n-1)d helps to find the required term directly.

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Arithmetic Progressions — Class 10 Mathematics Practice Questions Online

This page contains 816 practice MCQs for the chapter Arithmetic Progressions in Class 10 Mathematics. The questions are organized by difficulty — 271 easy, 376 medium, 169 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.