Question 1093779
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<pre>
They want you construct the 5-term geometric progression starting 16 and ending 81:

16 = a,  ar,  ar^2,  ar^3,  ar^4 = 81.


Hence,  r^4 = {{{(ar^4)/a}}} = {{{81/16}}}.


Thus  r = {{{root(4, 81/16)}}} = +/- {{{3/2}}} is the common ratio of the progression.


So, you have two ways to construct the required progression:


1)  16,  {{{16*(3/2)}}} = 24,  {{{24*(3/2)}}} = 36,  {{{36*(3/2)}}} = 54,  {{{54*(3/2)}}} = 81,    and


2)  16, -24, 36, -54, 81.
</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>.