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:

504

Step-by-step explanation:

Given,

common ratio (r) = 0.5

first term ($a_1$) is 256

Sum of first n terms in geometric series is given by the formula (r < 1):

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

Hence, sum of first 6 terms mean:

r = 0.5

a = 256

n = 6

Substituting, we get the answer to be:

$S_n=\frac{a(1-r^n)}{1-r}\\S_6=\frac{256(1-(0.5)^6)}{1-0.5}\\S_6=504$

The sum of first 6 terms is 504