Arithmetic Progressions

What you'll learn

Understand Arithmetic Progressions, the common difference, and the formulas for the nth term and the sum of n terms, explained with a staircase analogy, a fully worked example and a quick self-check quiz.

This chapter has

Arithmetic Progressions — solved practice questions

8 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   In an AP, the difference between any two consecutive terms is called the:

   • Acommon ratio
   • Bcommon difference
   • Cfirst term
   • Dlast term
   Show answer & solution

   Correct answer: (B) common difference

   The fixed (constant) difference between consecutive terms is the common difference (d).

2. Q2easy

   Which of the following is an AP?

   • A2, 5, 8, 11
   • B1, 2, 4, 8
   • C1, 4, 9, 16
   • D2, 6, 18, 54
   Show answer & solution

   Correct answer: (A) 2, 5, 8, 11

   2, 5, 8, 11 has a constant difference of 3, so it is an AP.

3. Q3easy

   The common difference of the AP 3, 7, 11, 15, … is:

   • A3
   • B3.5
   • C4
   • D7
   Show answer & solution

   Correct answer: (C) 4

   d = 7 − 3 = 4.

4. Q4medium

   The nth term of an AP with first term a and common difference d is:

   • Aa + (n−1)d
   • Ba + nd
   • Ca − (n−1)d
   • Dnd + a
   Show answer & solution

   Correct answer: (A) a + (n−1)d

   aₙ = a + (n−1)d.

5. Q5medium

   The 10th term of the AP 2, 5, 8, … is:

   • A26
   • B28
   • C29
   • D32
   Show answer & solution

   Correct answer: (C) 29

   a = 2, d = 3. a₁₀ = 2 + 9×3 = 2 + 27 = 29.

6. Q6medium

   The sum of first n terms of an AP is:

   • An(a + l)
   • Bn/2 × [2a + (n−1)d]
   • Cn × a + d
   • Dn/2 × (a + d)
   Show answer & solution

   Correct answer: (B) n/2 × [2a + (n−1)d]

   Sₙ = n/2 × [2a + (n−1)d].

7. Q7easy

   The sum of first 10 natural numbers is:

   • A50
   • B55
   • C60
   • D45
   Show answer & solution

   Correct answer: (B) 55

   S₁₀ = 10/2 × [2×1 + 9×1] = 5 × 11 = 55.

8. Q8easy

   In an AP, if a = 5 and d = 3, what is the 5th term?

   • A12
   • B15
   • C17
   • D20
   Show answer & solution

   Correct answer: (C) 17

   a₅ = 5 + 4×3 = 5 + 12 = 17.

Want the full set? Practise all 15 Arithmetic Progressions questions →