Arithmetic Progressions Exemplar — Class 10 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Arithmetic Progressions Exemplar" — 6 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Arithmetic Progressions Exemplar" — 6 important questions with detailed answers fo…
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NCERT Solutions for Class 10 Mathematics — Arithmetic Progressions Exemplar. Step-by-step answers to all 6 textbook questions from this chapter, written for CBSE board preparation and free to use.
Arithmetic Progressions Exemplar — All 6 Questions Solved
Q1. If first term a = 5 and common difference d = 3, find 10th term.
an = a + (n-1)d. a10 = 5 + (10-1)(3) = 5 + 27 = 32.
Q2. Find sum of first 20 terms of AP: 2, 5, 8, 11, ...
a = 2, d = 3, n = 20. Sn = n/2 [2a + (n-1)d] = 20/2 [2(2) + 19(3)] = 10[4 + 57] = 10(61) = 610.
Q3. Which term of AP 3, 8, 13, 18, ... is 78?
a = 3, d = 5. an = 78. 3 + (n-1)(5) = 78. (n-1)(5) = 75, so n - 1 = 15, thus n = 16. The 16th term is 78.
Q4. Insert 3 arithmetic means between 5 and 21.
If 3 means are inserted, sequence is 5, A1, A2, A3, 21 (5 terms total). Common difference d = (21 - 5)/(5 - 1) = 16/4 = 4. So means are 9, 13, 17.
Q5. Find sum of all two-digit natural numbers divisible by 4.
Sequence: 12, 16, 20, ..., 96. a = 12, d = 4, l = 96. n = (96 - 12)/4 + 1 = 21 + 1 = 22. Sn = n/2 (a + l) = 22/2 (12 + 96) = 11(108) = 1188.
Q6. If sum of n terms of AP is 3n^2 + 5n, find the AP.
Sn = 3n^2 + 5n. First term a = S1 = 3 + 5 = 8. For n ≥ 2, an = Sn - Sn-1 = 3n^2 + 5n - 3(n-1)^2 - 5(n-1) = 3(2n - 1) + 5 = 6n + 2. So a2 = 14, d = 6. AP: 8, 14, 20, 26, ...
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.