Question

Find the sum of the first 20 terms of the geometric sequence {2,6,18,54,…}.

Answer 1

Firstly find here r by dividing second term by first term..

Answer 2

3

Answer 3

Yep..

So, here n = 20 you are given with:

Use Sum formula:

\[Sum = \frac{a(r^n - 1)}{r - 1}\]

Answer 4

so the first term a = 2, ratio r = 3, number of terms n = 20

We know that sum of a GP Sn = a(r^n -1)/r-1

=> 2(3^20-1)/3-1

=> 2(3^20-1)/2

=> 3^20 - 1

which comes out to be

3486784401 -1 = 3486784400.

Answer 5

thanks

Answer 6

You are welcome dear..