Question 1114197
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Find the sum of n terms of a  G.P. whose nth term is {{{highlight(cross(3(2)^n-1))}}} 3*2^(n-1).
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            Notice that I edited your post to make it UNAMBIGUOUS.



<pre>
The geometric progression is

3,  6,  12,   24,  . . . 


The first term  is  {{{a[1]}}} = 3   and the common ratio is  r = 2.


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


{{{S[n]}}} = {{{a[1]*((r^n-1)/(r-1))}}} = {{{3*((2^n-1)/(2-1))}}} = {{{3*(2^n-1)}}}.


<U>Answer</U>.  The sum of the first n terms of the given progression  is  {{{S[n]}}} = {{{3*(2^n-1)}}}.
</pre>

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On geometric progressions, see introductory lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



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.