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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
10 years ago
Hello Student,

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

Thank you
Henry Kashyap
20 Points
10 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
10 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
7 years ago
That is option -D because 2d/a=1
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