Answer :
The answer to this question What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is (7/65/128)
Answer:
[tex]\frac{765}{128}[/tex]
Step-by-step explanation:
We have been given that 1st term of a geometric series is 3 and common difference is 1/2 . We are asked to find the sum of 1st 8 terms of the given series.
We will use geometric series formula to solve our given problem.
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Upon substituting our given values in the above formula we will get,
[tex]S_8=\frac{3(1-(\frac{1}{2})^8)}{1-\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1^8}{2}^8)}{\frac{2-1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{256-1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{255}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=3(\frac{255}{256}\times\frac{2}{1})[/tex]
[tex]S_8=3(\frac{255}{128})[/tex]
[tex]S_8=\frac{765}{128}[/tex]
Therefore, the sum of our given series is [tex]\frac{765}{128}[/tex].