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?

Answer 1

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 2

Answer:

$\frac{765}{128}$

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.

$S_n=\frac{a_1(1-r^n)}{1-r}$

Upon substituting our given values in the above formula we will get,

$S_8=\frac{3(1-(\frac{1}{2})^8)}{1-\frac{1}{2}}$

$S_8=\frac{3(1-\frac{1^8}{2}^8)}{\frac{2-1}{2}}$

$S_8=\frac{3(1-\frac{1}{256})}{\frac{1}{2}}$

$S_8=\frac{3(\frac{256-1}{256})}{\frac{1}{2}}$

$S_8=\frac{3(\frac{255}{256})}{\frac{1}{2}}$

$S_8=3(\frac{255}{256}\times\frac{2}{1})$

$S_8=3(\frac{255}{128})$

$S_8=\frac{765}{128}$

Therefore, the sum of our given series is $\frac{765}{128}$.