Ex 5.3, 9 - If sum of first 7 terms of an AP is 49, and 17 term is 289

Ex 5.3, 9 - Chapter 5 Class 10 Arithmetic Progressions - Part 2
Ex 5.3, 9 - Chapter 5 Class 10 Arithmetic Progressions - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 5.3, 9 If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms. We know that Sn = 𝑛/2 (2𝑎+(𝑛−1)𝑑) Sum of first 7 terms = 49 S7 = 7/2 (2𝑎+(𝑛−1)𝑑) 49 = 7/2 (2𝑎+(7−1)𝑑) 49 = 7/2 (2𝑎+6𝑑) (49 × 2)/7 "= 2a + 6d" "14 = 2a + 6d" (14 − 6𝑑)/2=𝑎 a = 7 – 3d Sum of first 17 terms = 289 S17 = 17/2 (2𝑎+(17−1)𝑑) 289 = 17/2 (2a + (17 – 1) d) 289 = 17/2 (2a + 16d) (289 × 2)/17 = 2a + 16d 34 = 2a + 16 d (34 − 16𝑑)/2 = a a = 17 – 8d From (1) and (2) 7 – 3d = 17 – 8d 8d – 3d = 17 – 7 5d = 10 d = 10/5 d = 2 Putting value of d in (1) a = 7 – 3d a = 7 – 3 ×2 a = 7 – 6 a = 1 Hence, a = 1 & d = 2 We need to find sum of first n terms We can use formula Sn = 𝒏/𝟐 (2a + (n – 1) d) Putting a = 1 & d = 2 = 𝑛/2 (2 × 1+(𝑛−1)2) = 𝑛/2(2+2𝑛−2) = 𝑛/2 (0 + 2n) = 𝑛/2 × 2n = n2

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.