Question

The common ratio in a geometric series is 0.5 and the first term is 256. Find the sum of the first 6 terms in the series

Answer 1

Answer:

The sum of the first 6 terms of the series is 504.

Step-by-step explanation:

Given that,

Common ratio in a geometric series is, r = 0.5

First term of the series, a = 256

We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:

$a,ar^1,ar^2,ar^3......$

The sum of n terms of a GP is given by :

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

Here, n = 6

$S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504$

So, the sum of the first 6 terms of the series is 504.