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  4. If twice the 11th term of an AP is equal to 7 times its 21st term, then its 25th term is equal to

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Q. If twice the $11^{th}$ term of an AP is equal to $7$ times its $21^{st}$ term, then its $25^{th}$ term is equal to

J & K CETJ & K CET 2005

Solution:

$11^{th}$ term of an $ AP=a+(11-1)\,d=a+10d $
$21^{st}$ term of an $ AP=a+20d $ and
$25^{th}$ term of an $ AP=a+24d $
According to the given condition,
$ 2(a+10d)=7(a+20d) $
$ \Rightarrow $ $ 2a+20d=7a+140d $
$ \Rightarrow $ $ -5a=120d $
$ \Rightarrow $ $ a=-\frac{120}{5}\,d=-24d $
$ \therefore $ $25^{th}$ term $ =-24d+24d=0 $