Question

What is the sum of the series? 4+12+36+108+...+8748

Answer 1

Answer:

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

Step-by-step 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 ,

$a_n=a_0\times r^{n-1}$

and sum of series is given by  $S_n=\frac{a(r^{n}-1)}{r-1}$

12 = 4× 3

36 = 4 × 3 × 3

108 = 4 × 3 × 3 × 3

and so on

so $a_n=a_0\times r^{n-1}$

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 $\sum _{n=1}^8\:4\times 3^n$ having common ratio r = 3  

Thus, sum of series is

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

we have $S_8=\frac{4(3^{8}-1)}{3-1}$

Simplify, we have,

$S_8=\frac{4(3^8-1)}{2}=13120$

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

Answer 2

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