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Consider an A.P. with first term 'a' and the common difference 'd'. Let Sk denote the sum of its first K terms. If x kx S S is independent of x, then (A) a = d/2 (B) a = d (C) a = 2d (D) none

Consider an A.P. with first term 'a' and the common difference 'd'. Let Sk denote the sum of its first K
terms. If
x
kx
S
S
is independent of x, then
(A) a = d/2 (B) a = d (C) a = 2d (D) none

Grade:11

4 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
8 years ago
Hello Student,

can you please specify the condition in the question properly becoz its not clear

Thank you
Henry Kashyap
20 Points
8 years ago
okay here the question again...Q.Consider an A.P. with first term 'a' and the common difference 'd'. Let Sk denote the sum of its first Kterms. If Skx/Sx is independent of x then which one is correct ?A) a = d/2 (B) a = d (C) a = 2d (D) none
thankyou in advance
Nishant Vora IIT Patna
askIITians Faculty 2467 Points
8 years ago
Hello student,

\frac{Skx}{Sx} = \frac{\frac{kx}{2} (2a + (kx-1)d)}{\frac{x}{2}(2a + (x-1)d)}

\frac{Skx}{Sx} = \frac{k(2a + (kx-1)d)}{(2a + (x-1)d)}

\frac{Skx}{Sx} = \frac{k(2a -d + kxd)}{(2a - d + xd)}
Now this will be independent of ‘x‘ only when 2a=d
Option (A)
Herb
23 Points
6 years ago
That is option -D because 2d/a=1
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