Question

In an A.P if $d=4,n=7$ and $t_n=4$ then find $S_n$

Answer 1

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

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

$\Rightarrow 4=a+24$

$\therefore a=4-24=-20$

$\therefore S_n=\frac{n}{2}(a+l)$

$=\frac{7}{2}(-20+4)=\frac{7}{2}\times -16=-56$

$\therefore S_n=-56$