Question

What is the sum of the series?

4+12+36+108+...+8748

Answer 1

You would add them all up and then you answer will be 8,908.

4 + 12 =
16 + 36 =
52 + 108 =
160 + 8, 748 =
8, 908.


I hope I helped you. :)

- Shelly O

Answer 2

Sum of series 4+12+36+108+...+8748 is 13120

Explanation:

Given series 4+12+36+108+...+8748

We have to find the sum of the given series.

A geometric sequence has a common ratio r and is defined by ,

`a_n=a_0* r^(n-1)`

and sum of series is given by
`S_n=(a(r^(n)-1))/(r-1)`

12 = 4× 3

36 = 4 × 3 × 3

108 = 4 × 3 × 3 × 3

and so on

so
`a_n=a_0* r^(n-1)`

we have
`a_n=8748, a_0=4,r=3`

Substitute ,and solve for r , we have n= 8

Thus, the series can be represented as
`\sum _(n=1)^8\:4* 3^n` having common ratio r = 3

Thus, sum of series is

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

we have
`S_8=(4(3^(8)-1))/(3-1)`

Simplify, we have,

`S_8=(4(3^8-1))/(2)=13120`

Sum of series 4+12+36+108+...+8748 is 13120