SOLUTION: Find the sum of n terms of a G.P. whose nth term is 3(2)^n-1

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum of n terms of a G.P. whose nth term is 3(2)^n-1      Log On


   

Question 1114197: Find the sum of n terms of a G.P. whose nth term is 3(2)^n-1
Found 2 solutions by amalm06, ikleyn:
Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
|r|=3/2 > 1, so the series diverges

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the sum of n terms of a G.P. whose nth term is highlight%28cross%283%282%29%5En-1%29%29 3*2^(n-1).
~~~~~~~~~~~~~


            Notice that I edited your post to make it UNAMBIGUOUS. 


The geometric progression is

3,  6,  12,   24,  . . . 


The first term  is  a%5B1%5D = 3   and the common ratio is  r = 2.


Apply the general formula for the first n terms of an geometric progression


S%5Bn%5D = a%5B1%5D%2A%28%28r%5En-1%29%2F%28r-1%29%29 = 3%2A%28%282%5En-1%29%2F%282-1%29%29 = 3%2A%282%5En-1%29.


Answer.  The sum of the first n terms of the given progression  is  S%5Bn%5D = 3%2A%282%5En-1%29.

----------------
On geometric progressions, see introductory lessons in this site
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Geometric progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.