# In a geometric sequence, the first term is 3 and the sum of the first 3 terms is 21, find the sum of the first 7 terms.

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Expert Answers

thilina-g | Certified Educator

A geometric series can be given as below,

`s_n = a+ar+ar^2+ar^3+.......+ar^(n-1)`

a - First term

r - common ratio

The sum of a geomatric series is given by,

`s_n = a(1-r^n)/(1-r)`

First term = a = 3

Sum of first three term = 21

`3+3r+3r^2 = 21`

`r^2+r+1 =7`

`r^2+r-6 = 0`

(r+3)(r-2) =0

We know r!=-3, therefore r=2.

For the geometric series,

a =3 and r = 2.

Sum of first seven terms,

`s_n = 3((1-2^7)/(1-2))`

`S_n = 381`

**The sum of first seven series is 381.**