Question

In an A.P the first term is $2$ and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is $-112$

Answer 1

In $A.P,$ First term $,a=2$

Let the common difference be $d$

From the given condition,

$\frac{5}{2}(2+2+4d)=\frac{1}{4}\times \frac{5}{2}\left(\right(2+5d+2+9d)$

$16+16d=4+14d⟹d=-6$

$20$th term is $a+19d=2+19(-6)=-112$