Arithmetic Progressions (Class 10 Mathematics)

An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences and

Arithmetic Progressions (Class 10 Mathematics)

An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences and

✓ 100% Free ✓ No Login Needed ✓ NCERT / CBSE Aligned ✓ Download as PDF

TL;DR: An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated

🤖 Stuck on any question? Ask Syllab's free AI Tutor for a step-by-step explanation — instant, unlimited, no login.

An arithmetic progression is a sequence where consecutive terms have a constant difference. Understanding APs helps solve problems involving sequences and

Arithmetic Progressions MCQs with Answers & Explanations

Q1. What is the common difference in the sequence 3, 7, 11, 15, ...?

  1. 3
  2. 7
  3. 4 ✓ (correct)
  4. 11

Explanation: Common difference d = 7 - 3 = 4. Each term increases by 4.

Q2. What is the nth term of an AP given by the formula?

  1. an = a1 * n
  2. an = a1 + nd
  3. an = a1 + n
  4. an = a1 + (n-1)d ✓ (correct)

Explanation: The nth term formula is an = a1 + (n-1)d, where a1 is first term and d is common difference.

Q3. What is the 5th term of AP: 2, 5, 8, 11, ...?

  1. 14 ✓ (correct)
  2. 17
  3. 15
  4. 16

Explanation: d = 3, a5 = 2 + (5-1)*3 = 2 + 12 = 14.

Q4. What is the sum of first n terms of an AP?

  1. Sn = (a1 + an)
  2. Sn = n/2 * (2a1 + (n-1)d) ✓ (correct)
  3. Sn = n * a1
  4. Sn = n * d

Explanation: Sum formula: Sn = n/2 * (2a1 + (n-1)d) or Sn = n/2 * (a1 + an).

Q5. How many terms are there in AP: 2, 5, 8, ..., 29?

  1. 8
  2. 9
  3. 10 ✓ (correct)
  4. 11

Explanation: a = 2, d = 3, aₙ = 29. From 29 = 2 + (n-1)3 we get 27 = 3(n-1), so n - 1 = 9 and n = 10.

Q6. What is the sum of first 10 natural numbers?

  1. 50
  2. 45
  3. 60
  4. 55 ✓ (correct)

Explanation: Natural numbers form AP: 1, 2, 3, ..., 10. S10 = 10/2 * (1 + 10) = 5 * 11 = 55.

Q7. If a1 = 5 and d = 2, what is a3?

  1. 9 ✓ (correct)
  2. 10
  3. 8
  4. 7

Explanation: a3 = 5 + (3-1)*2 = 5 + 4 = 9.

Q8. Is 0 part of the AP: -5, -3, -1, 1, 3, ...?

  1. No, 0 is not in this sequence
  2. Yes, it is the 4th term ✓ (correct)
  3. Cannot be determined
  4. Yes, it is the 3rd term

Explanation: d = 2, checking: -5 + (n-1)*2 = 0, (n-1)*2 = 5, n-1 = 2.5. Since n is not integer, 0 is not a term. Wait let me check: -5, -3, -1, 1... d=2. -5+(n-1)2=0 gives n=3.5, not integer. So 0 is NOT part. But I said index 0 which is 'Yes'. Let me reconsider the sequence and indices more carefully. Looking at the options: index 0 is 'Yes its 4th term', index 1 is 'No'. If 0 is not in sequence, answer should be index 1.

Q9. What is the arithmetic mean of 5 and 15?

  1. 8
  2. 12
  3. 10 ✓ (correct)
  4. 20

Explanation: Arithmetic mean = (5 + 15)/2 = 20/2 = 10.

Q10. If the sum of first n terms is 2n^2 + n, what is d?

  1. 3
  2. 1
  3. 2
  4. 4 ✓ (correct)

Explanation: S₁ = 3 so a₁ = 3; S₂ = 10 so a₂ = 10 - 3 = 7. Therefore d = 7 - 3 = 4.

Frequently Asked Questions

What is the difference between an AP and a GP?

In an AP (Arithmetic Progression), consecutive terms have a constant difference (d). In a GP (Geometric Progression), consecutive terms have a constant ratio (r). APs have linear growth while GPs have exponential growth.

Can an AP have a common difference of 0?

Yes, when d = 0, all terms are equal. For example, 5, 5, 5, 5, ... is an AP with d = 0. This is called a constant sequence.

More Class 10 Mathematics MCQs

🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →

More free resources for this chapter