SOLUTION: Find the sum of the first 20 terms of the series 1+3+9+27... Please explain with a formula. Thank you!

Question 472498: Find the sum of the first 20 terms of the series
1+3+9+27...
Please explain with a formula. Thank you!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I will show you the formula plus how it is derived so that you don't blindly memorize it. Blindly memorizing formulas is a common pitfall students make, and it makes students less likely to actually "understand" the material.

Let

Then,

We can do 3S - S and obtain lots of cancellation:

To generalize, you would let the common difference be something like "r" then the denominator of 2 would be replaced with r-1. Also, for an arbitrary exponent n (here n = 19) the 20 would be replaced with n+1.
RELATED QUESTIONS
I am having trouble with this problem, could you please help me. 3) Use the geometric... (answered by sdmmadam@yahoo.com)

find the sum of the first five terms in the geometric series -3/2+1-2/3+... A. 55/54 (answered by ewatrrr)

I understand the examples you have given to find the sum of sequences but i have a... (answered by stanbon)

please help...thanks Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,�to find the (answered by aaaaaaaa)

Algebra 2 question! Help me please! I have a test on this stuff later today and I am very (answered by Fombitz)

3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following. (answered by sdmmadam@yahoo.com)

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,�to find the following: a) What... (answered by mukhopadhyay)

find the sum of first 10 terms for the series of -1 , -8 , -27 , -64 ,... (answered by Fombitz)

Find the sum of the first 20 terms of 3, -9, 27, -81,... (answered by Edwin McCravy)