Question

Determine the 9th term of an A.P whose third term is $16$ and the difference of $5th$ term from $7th$ term is $12$.

Answer 1

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