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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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For an AP with first term $a$ and common difference $d$, if $\large\frac{S_{nx}}{S_{x}}\:(S_{r}$ denotes sum upto $r$ term$)$ is independent of $x$ then,


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Answer : (b) $\;a=\large\frac{d}{2}$
Explanation : $\;\large\frac{S_{nx}}{S_{x}}=\large\frac{\large\frac{nx}{2}\;[2a+(nx-1)d]}{\large\frac{x}{2}\;[2a+(x-1)d]}=k\;(say)$
Since above term is independent of x
answered Jan 23, 2014 by yamini.v

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