Question

The third terms of an AP is 7 and the 9th term of AP exceeds 3 times of the 3 rd term by 2 . Find the first term and it's common difference and sum of the 20 terms

Answer 1

A3=7

A9=3(A3)+2

That means, A9= 3(7)+2 = 21+2 = 23.

Now as we know, A3 = A + 2d AND A9 = A + 8d

Therefore, 23 = A + 8d

- 7 = A + 2d

Gives,6d = 16

Therefore d=8/3.

And now A3 = A + 2(8/3)

7- 16/3 = A

And, A = 5/3.

And S20 = 20/2(2*5/3+(19)8/3)

S20 = 10 ( 10/3 + 152/3)

Therefore,S20 = 1620/3 = 540.