Question

If the sum of first 4 terms of an A.P. is 40 and that of first 14 terms is 280, find the sum of its first x terms.

Answer 1

Sn = sum of n terms of an A.P. = n/2 [ 2a + (n-1)d]

A/Q    

 S₄ = 40 = 4/2 [2a + 3d]  =  2a + 3d = 20            ...........(1)

and

S₁₄ = 280 = 14/2 [2a + 13d]  = 2a + 13d = 40         .........(2)

solving (1) and (2)

gives  a = 7    and d= 2

so Sn = n/2[ 2(7) + (n-1)2]  = 7n + n² - n = n² + 6n

hope my solution is true.

I HOPE ITS HELPFUL