SOLUTION: This is a homework problem that I cannot seem to solve. It states to: Find the sum of the first 20 terms of the series 1 + 8 + 64 + 512 + . . . Can you please help? Thank

Algebra ->  Sequences-and-series -> SOLUTION: This is a homework problem that I cannot seem to solve. It states to: Find the sum of the first 20 terms of the series 1 + 8 + 64 + 512 + . . . Can you please help? Thank       Log On


   

Question 116982This question is from textbook
: This is a homework problem that I cannot seem to solve. It states to:
Find the sum of the first 20 terms of the series
1 + 8 + 64 + 512 + . . .
Can you please help? Thank you in advance. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that each term is increasing exponentially. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.

First divide the 2nd term 8 by the 1st term 1 to get
8%2F1=8

Now divide the 3rd term 64 by the 2nd term 8 to get
64%2F8=8

Now divide the 4th term 512 by the 3rd term 64 to get
512%2F64=8

So if we pick any term and divide it by the previous term, we'll always get . This is the common ratio between the terms. So this means that r=8.

Now since we've started at 1, this means that a=1


Now remember, the formula for the sum of a geometric sequence is

a%281-r%5En%29%2F%281-r%29

1%281-8%5E20%29%2F%281-8%29 Plug in a=1, r=8, and n=20 (since we want to find the sum of the first 20 terms)


%281-8%5E20%29%2F%28-7%29 Subtract



%281-1.153%2A10%5E18%29%2F%28-7%29 Raise 8 to the 20th power to get 1.153%2A10%5E18


%28-1.153%2A10%5E18%29%2F%28-7%29 Subtract


1.647%2A10%5E17 Divide


So the sum of the first 20 terms is 1.647%2A10%5E17