Question

What is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?

Answer 1

The terms of the geometric sequence are 1,3,9, ...,

The first term is a = 1
The common ratio is r = 3.

The sum of the first 10 terms is
$S_{10} = \frac{1(1-3^{10} )}{1-3} =29524$

Answer:  29524

Answer 2

Answer: 29524

Step-by-step explanation:

Given geometric sequence : 1, 3, 9, …........................

First term of G.P. $a = 1$

Second term of G.P.$a_2=3$

Common ratio =$r=\frac{a_2}{a}=\frac{3}{1}=3$

We know that the sum of the geometric sequence with n terms is given by :-

$S=\frac{a(r^n-1)}{r-1}$ for |r|>1

Substitute a = 1 , r =3 and n=10 , we get

$S=\frac{1(3^(10)-1)}{3-1}\\\\=\frac{59049-1}{2}\\\\=-\frac{59048}{2}\\\\\Rightrrow\ S=29524$