Question 31 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 10, 2025 by Teachoo

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Question 31 The sum of first n terms of an AP is 5𝒏2 − 𝒏. Find the nth term of the AP.Given Sn = 5n2 – n Taking n = 1 S1 = 5 × 12 – 1 = 5 – 1 = 4 ∴ Sum of first term of AP is 4 Taking n = 2 in Sn S2 = 5 × 22 – 2 = 5 × 4 – 2 = 18 ∴ Sum of first 2 terms is 18 But sum of first term will be the first term So, First term = a = 4 Finding 2nd term Sum of first 2 terms = 18 First term + Second term = 18 4 + a2 = 18 a2 = 18 – 4 a2 = 14 Hence, Common difference = d = Second term – First term = 14 – 4 = 10 Thus, our AP looks like 4, 14, 24, … We need to find nth term We know that an = a + (n – 1) d = 4 + (n − 1) × 10 = 4 + 10n – 10 = 10n – 6 Note: We could have also done an = Sn – Sn–1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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