In an A.P., if $d = –4,\ n = 7,\ a_n=4$, then find $a$.

Given: In an A.P., if $d = –4,\ n = 7,\ a_n=4$.

To do: To find the value $a$.

Solution:

As known, $n^{th}$ term of A.P. $a_n=a+( n-1)d$

On substituting the values,

$\Rightarrow 4=a+( 7-1)( -4)$

$\Rightarrow 4=a-24$

$\Rightarrow a=24+4$

$\Rightarrow a=28$

Thus, $a=4$.