Question

The $9^{th}$ term of an A.P. is equal to $6$ times its second term. If its $5^{th}$ term is $22$, then find the A.P.

Answer 1

Let $a=$ first term of A.P., $d=$common difference

$n^{th}$ term, $a_n=a+(n-1)d$; Given $a_9=6a_2$

$\Rightarrow a+8d=6(a+d)\Rightarrow 5a=2d$

$\Rightarrow a=\frac{2d}{5}$

and $a_5=22$

$\Rightarrow a+4d=22$

$\Rightarrow \frac{2d}{5}+4d=22$

$\Rightarrow 22d=5\times 22$

$\Rightarrow d=5$

$\Rightarrow a=2$

$\Rightarrow$ A.P. $:2,7,12,17,....$.