Question 1118014
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<pre>
Geometric progression with the first term of 1 and the common ratio of 5.


The number of terms is 6:   {{{5^(6-1)}}} = {{{5^5}}} = 3125.


Use the formula for the sum of the first n terms of a Geom. progression with the first term a and the common ratio of r:


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


Substitute the given values and calculate:


{{{S[5]}}} = {{{1*(5^6-1)/(5-1)}}} = 3906.
</pre>

Solved.


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On geometric progressions, &nbsp;see the 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.