Question

Prove that the sequence, whose general term is $a_n={2.3}^n$, is a geometric progression and find the stint of the first eight terms.

Answer 1

let $a_n={2.3}^n,a_{n+1}={2.3}^{n+1},a_{n+2}={2.3}^{n+2}$

$⟹\frac{a_{n+1}}{a_n}=\frac{a_{n+2}}{a_{n+1}}=3$ Clearly it is in a GP

it's first three terms are $6,18,54$