Question

The first, the third, and the fifth term of a geometric progression are equal to the first, the fourth, and the sixteenth term of a certain arithmetic progression respectively. Calculate the fourth term of the arithmetic progression if its first term is $5$.

Answer 1

Given $a,ar,a{r}^2$are equal to $a,a+3d,a+15d$ respectively

$⟹5\left(ar\right)=4a+a{r}^2⟹r^2-5r+4=0⟹r=1,4$

$⟹$Fourth term of an AP is $5\text{or}20$