Question

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

• A. 24
• B. 120
• C. 0
• D. None of these

Answer 1

Answer: (C)

$11^{th}$ 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 $=-24d+24d=0$