Question

If the sum of first k terms of an A.P. is 1/ 2 (3k² + 7k), write its kth term. Hence find its 20th term.

Answer 1

Let ak denotes the nth terms  and Sk denotes the sum of the first k terms of  given AP.

Given:
Sk =1/ 2 (3k² + 7k)

ak = Sk - S(k -1)
= 1/ 2 (3k² + 7k) - [1/ 2 (3(k-1)² + 7(k-1)]
= 1/ 2 (3k² + 7k) - [½ 3(k² +1-2k) +7k-7]
= 1/ 2 (3k² + 7k) - [½ (3k² +3 -6k+7k-7)]
= 1/ 2 (3k² + 7k) - [½ (3k² +k- 4)]
= ½ [(3k² + 7k) - (3k² +k- 4)]
= ½ [3k² + 7k - 3k² - k + 4)]
= ½ [6k + 4)]

ak= 3k +2
kth term of an AP = ak= 3k +2

20th term of an AP (a20) = a20= 3(20) +2
a20 = 60 +2= 62
a20 = 62

Hence,its 20 term (a20) = 62.

HOPE THIS WILL HELP YOU.....

Answer 2

hope this helps you quickly