Question

Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

Answer 1

`\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot (1)/(2)}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...`

so as you can see the common ratio is 2, and the first term is 1/2,

Answer 2

The sum of 8 term of the series is
`(255)/(2)` or 127.5

Explanation:

Given: The series
`(1)/(2)` + 1 +2 +4 + ...

We need to find the sum of 8 term

Common ratio, r
`=(2)/(1)= 2`

First term,
`a=(1)/(2)`

n=8

Formula:

`S_n=(a(r^n-1))/((r-1))`

Substitute the value of a, r and n into formula

Sum of 8th term of the sequence

`S_8=(1/2(2^8-1))/(2-1)`

`S_8=(255)/(2)`

Hence, The sum of 8 term of the series is
`(255)/(2)` or 127.5