Question

In an A.P. if $d=-2$, $T_{22}=-39$, find $a$

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 $t_{22}=-39$ and the difference is $d=-2$, therefore,

$t_n=a+(n-1)d\Rightarrow -39=a+(22-1)(-2)\Rightarrow -39=a+(21\times -2)\Rightarrow -39=a-42\Rightarrow a=-39+42=3$

Hence, $a=3$