Question

The 5th and 15th terms of an A.P. are 13 and - 17 respectively. Find the sum of first 21 terms of the A.P.
​

Answer 1

Answer:

Given: a5 = 13 and a15 = -17 and n = 21 We know that, a5 = a + 4d = 13 …(i) and a15 = a + 14d = -17 …(ii) Solving the linear equations (i) and (ii), we get a + 4d – a – 14d = 13 – (-17) ⇒ -10d = 13 + 17 ⇒ -10d = 30 ⇒ d = -3 Putting the value of d in eq. (i), we get a + 4(-3) = 13 ⇒ a = 13 + 12 = 25 Now, we have to find the sum of first 21 terms. ⇒ S21 = 21 [25 + 10 × (-3)] ⇒ S21 = 21 [-5] ⇒ S21 =-105Read more on Sarthaks.com - https://www.sarthaks.com/952184/the-5th-and-15th-terms-of-an-a-p-are-13-and-17-respectively-find-the-sum-of-first-21-terms-of-the