Question

In an A.P. if $a=13$, $T_{15}=55$, find $d$.

Answer 1

We know that the formula for the nth term is $t_n=a+(n-1)d$, where $a$ is the first term, $d$ is the common difference.

It is given that the nth term is $t_{15}=55$ and the first term is $a=13$, therefore,

$t_n=a+(n-1)d\Rightarrow 55=13+(15-1)d\Rightarrow 55=13+14d\Rightarrow 14d=55-13\Rightarrow 14d=42\Rightarrow d=\frac{42}{14}=3$

Hence, $d=3$