Question

Three numbers whose sum is equal to $28$ form a geometric progression. If we add $3$ to the first number and $1$ to the second and subtract $5$ from the third number, the resulting numbers will form an arithmetic progression. Find the numbers.

Answer 1

let $\frac{a}{r},a,ar$ be 3 terms

sum$=28$

$⟹2a+2=\frac{a}{r}+ar-2$

$⟹3a+2=\frac{a}{r}+a+ar-2$

$⟹a=8$

$⟹r=\frac{-1}{2},2$

Numbers $4,8,16$