Question 1100227
.
<pre>
{{{a[3]}}} = {{{a[1]*r^2}}},    (1)

{{{a[8]}}} = {{{a[1]*r^7}}}.    (2)

====================================>

{{{a[8]/a[3]}}} = {{{4374/18}}} = 243 = {{{(a[1]*r^7)/(a[1]*r^2)}}} = {{{r^5}}}  ====>


r = {{{root(5,243)}}} = 3.


Thus the common ratio is 3.


Then the first term  is  {{{a[1]}}} = {{{a[3]/r^2}}} = {{{18/3^2}}} = 2.


<U>Answer</U>.  The first term  is 2.  The common ratio is  3.

         The n-th term is {{{a[n]}}} = {{{2*3^(n-1)}}}.
</pre>

Solved.


----------------
There is a bunch of lessons on geometric progressions in this site

&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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-geometric-progressions.lesson>Solved problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Fresh-sweet-and-crispy-problem-on-arithmetic-and-geometric-progressions.lesson>Fresh, sweet and crispy problem on arithmetic and geometric progressions</A>



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.