Question

consider an ap with first term a and common difference d let sk denoted the sum of first k terms if
$sk$

Answer 1

Skx = kx/2 (2a + (kx-1)d)

Sx = x/2 (2a + (x-1)d)

Skx/Sx = [kx/2 (2a + (kx-1)d)] / [x/2 (2a + (x-1)d)]

= [k (2a + (kx-1)d)] / [(2a + (x-1)d)]

For Skx/Sx to be independent of x, 2a – d = 0.

2a – d = 0 ⇒ 2a = d ⇒ a = d/2.

Answer 2

Step-by-step explanation:

when it is independent of x then a =d/2