Question 1180308
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The second term of an exponential sequence is 9 while the fourth term is 81. 
Find the common ratio and first term
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<pre>
The ratio   {{{a[4]/a[2]}}}  is  {{{r^2}}},  where r is the common ratio.


So,  r^2 = 9,  which implies  r = {{{sqrtr(9)}}} = +/- 3.


Thus for r we have two possible answers, the values  3  and  -3.



    If r = 3,   then the first term is  {{{a[1]}}} = 9/3 = 3.


    If r = -3,  then the first term is  {{{a[1]}}} = 9/(-3) = -3.


<U>ANSWER</U>.  There are two solutions:   a)  r= 3, {{{a[1]}}} = 3,  and  b)  r= -3, {{{a[1]}}} = -3.
</pre>

Solved.


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Standard name/term for the exponential sequence is a Geometric progression/sequence.



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.