Question

Determine the A.P. whose third term is 16 and the difference of $5^{th}$ term from $7^{th}$ is 12.

Answer 1

$a_3=a+(3-1)d=a+2d=\mathrm{16.........}\left(i\right)$
$a_7-a_5=12...................\left(ii\right)$
$a_7=a+6d$
$a_5=a+4d$
$\Rightarrow (a+6d)-(a+4d)=12$
$\Rightarrow a+6d-a-4d=12$
$\Rightarrow 2d=12$
$\Rightarrow d=6$
Put $d=6$ in equation (i)
$a=16-12$
$\Rightarrow a=4$
$\therefore$ AP is $4,10,16,22,28,......$