Question

For a given A.P, $T_7=12$ and $T_{12}=72,$ then $d=$ _______

Answer 1

We know that the formula for $n^{th}$ term of an A.P is :

$T_n=a+(n-1)d$

$T_7=12$

$a+(7-1)d=12$

$a+6d=12$ ……..$\left(1\right)$

$T_{12}=72$

$a(12-1)d=72$

$a+11d=72$ ……….$\left(2\right)$

Subtracting $\left(1\right)$ from $\left(2\right)$, we get

$5d=60$

$\Rightarrow d=12$