Question

The sum of first n terms of a sequence is $5(3^{n}-1)$, show that it is a G.P.

Answer 1

it is given that,

sum of n terms of the sequence, $S_n=5(3^n-1)$

or, $S_n=\frac{10(3^n-1)}{2}$


we know, sum of n terms in G.P is given by,

$S_n=\frac{a(r^n-1)}{2}$

where a is first term and r is the common ratio.

compare the both equations ,

it is clearly shown that given sequence is in geometric progression where a = 10, r = 3 .

some terms in sequence are : 10, 30, 90, 270 ....