Question

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

Answer 1

Answer: 29524

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=(a_2)/(a)=(3)/(1)=3`

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

`S=(a(r^n-1))/(r-1)` for |r|>1

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

`S=(1(3^(10)-1))/(3-1)\\\\=(59049-1)/(2)\\\\=-(59048)/(2)\\\\\Rightrrow\ S=29524`

Answer 2

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) = (1(1-3^(10) ))/(1-3) =29524`

Answer: 29524