Check sibling questions

Ex 5.3, 8 - Find sum of first 51 terms of an AP whose second

Ex 5.3, 8 - Chapter 5 Class 10 Arithmetic Progressions - Part 2
Ex 5.3, 8 - Chapter 5 Class 10 Arithmetic Progressions - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 5.3, 8 Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively. We know that an = a + (n – 1) d From (1) & (2) 14 – d = 18 – 2d Given 2nd term is 14 a2 = a + (2 – 1) d 14 = a + d 14 – d = a a = 14 – d Given 3rd term is 18 a3 = a + (3 – 1) d 18 = a + 2d 18 – 2d = a a = 18 – 2d 2d – d = 18 – 14 d = 4 Putting value of d in (1) a = 14 – d a = 14 – 4 a = 10 Now, we need to find sum of first 51 terms We can use formula Sn = 𝒏/𝟐 [2a + (n – 1) d] Putting n = 51 , a = 10 & d = 4 S51 = 51/2 (2 × 10 + (51 − 1) × 4) S51 = 51/2 (20 + 50 × 4) S51 = 51/2 × (20 + 200) S51 = 51/2 × 220 S51 = 51 × 110 S51 = 5610 Hence, the sum of first 51 terms is 5610

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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.