Question

Determine an $A.P$ whose third term is $9$ and when fifth term is subtracted from $8th$ term we get $6$.

Answer 1

Let the first term of A.P be $a$ and common difference be $d$

Here given$t_3=a+2d=9$ ......$\left(1\right)$

Given:$t_8-t_5=6$

$\Rightarrow a+7d-a-4d=6$

$\Rightarrow 3d=6$

$\therefore d=2$ .......$\left(2\right)$

Substituting this value of $d=2$ from $\left(2\right)$ in $\left(1\right)$, we get

$a+2\left(2\right)=9$

or $a=9-4=5$

So,A.P is $5,7,9,11,...$