Question

Find the sum of the first six terms of a geometric progression .​

Answer 1

Question:

Find the sum of the first six terms of a geometric progression.

1,3,9,....

Answer:

$S_6 = 364$

Step-by-step explanation:

For a geometric progression, the sum of n terms is:

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

In the given sequence:

$a = 1$

$r = 3/1 =3$

$n = 6$

So:

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

$S_6 = \frac{1 * (3^6 - 1)}{3 - 1}$

$S_6 = \frac{3^6 - 1}{2}$

$S_6 = \frac{728}{2}$

$S_6 = 364$