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:
[tex]a,ar^1,ar^2,ar^3......[/tex]
The sum of n terms of a GP is given by :
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Here, n = 6
[tex]S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504[/tex]
So, the sum of the first 6 terms of the series is 504.
