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

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) (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

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

Now divide the 4th term 512 by the 3rd term 64 to get

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 .

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

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

Plug in a=1, r=8, and n=20 (since we want to find the sum of the first 20 terms)

Subtract

Raise 8 to the 20th power to get

Subtract

Divide

So the sum of the first 20 terms is
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