Question 1109439
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<pre>
{{{a[1]+a[2]+a[3]+a[4]}}} = {{{a[1]*(1 + r + r^2 + r^3)}}} = 15.       (1)    (given)

{{{a[5]+a[6]+a[7]+a[8]}}} = {{{a[1]*r^4*(1 + r + r^2 + r^3)}}} = 240.    (2)    (given)


Now divide eq(2) by eq(1). You will get


{{{r^4}}} = {{{240/15}}} = 16.


The positive constant ratio is  r = 16^(1/4) = 2.
</pre>

Solved.


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On geometric progressions, 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.