ICSE Class 10 Mathematics: Arithmetic and Geometric Progression — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: Find the 20th term of the AP: 3, 7, 11, 15, ...
  Ans: a = 3, d = 7-3 = 4, n = 20. aₙ = a + (n-1)d = 3 + (20-1)(4) = 3 + 76 = 79.
• Q: Find the sum of first 15 terms of AP: 5, 8, 11, ...
  Ans: a = 5, d = 3, n = 15. Sₙ = n/2[2a + (n-1)d] = 15/2[10 + 14(3)] = 15/2[10 + 42] = 15/2 × 52 = 390.
• Q: The 3rd term of a GP is 18 and the 6th term is 486. Find the GP.
  Ans: a₃ = ar² = 18 ... (i). a₆ = ar⁵ = 486 ... (ii). Dividing (ii) by (i): r³ = 486/18 = 27. r = 3. From (i): a(9) = 18, a = 2. GP: 2, 6, 18, 54, 162, 486, ...

Long Answer / Application Questions (4-6 Marks)

• Q: Insert 3 arithmetic means between 4 and 20.
  Ans: AP: 4, _, _, _, 20. a = 4, a₅ = 20. a₅ = a + 4d = 20. 4 + 4d = 20. d = 4. The 3 arithmetic means are: 8, 12, 16.

Exam Tips for This Chapter

• Revise all definitions and laws from Arithmetic and Geometric Progression — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Arithmetic and Geometric Progression — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Arithmetic and Geometric Progression carries 8-12 marks in the board exam