Question 1185788
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<pre>

Use the standard formula for the sum of n first terms of a geometric progression


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


where "a" is the first term, r is the common ratio.


In your case,  n = 8, a = 1, r = {{{-2/3}}}.


So,  {{{S[8]}}} = {{{1*((-2/3)^8-1)/(-2/3-1))}}} = {{{((2^8/3^8-1)/(-5/3))}}} = {{{(2^8 - 3^8)/(3^8*(-5/3))}}} = 

                = {{{(3/5)*((3^8-2^8)/3^8)}}} = {{{(1/5)*((3^8-2^8)/3^7)}}} = {{{6305/(5*3^7)}}} = {{{1261/3^7}}} = 0.5766  (rounded).   <U>ANSWER</U>
</pre>

Solved.


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On geometric progressions, &nbsp;see introductory lessons

&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>

in this site.


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.