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If Sn denote the sum of n terms of an AP with first term a and common difference d such that Sx÷Skx is independent of x, then d=?

Posted by Sunidhi Singh 5 years, 4 months ago

CBSE > Class 10 > English Language and Literature

1 answers

Gaurav Seth 5 years, 4 months ago

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

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

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

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

For S_kx/S_x to be independent of x, 2a – d = 0.

2a – d = 0 ⇒ 2a = d ⇒ a = d/2.

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CBSE > Class 10 > English Language and Literature