Question 1202405
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The fifth term of a geometric progression is 1 and the common ratio is ½. 
Find (a) the {{{highlight(cross(eight))}}} <U>eighth</U> term and (b) an expression for the nth term.
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<pre>
(a)  The 8-th term is  {{{a[8]}}} = {{{a[5]*(1/2)^3}}} = {{{1/8}}}.     <U>ANSWER</U>


     The 1-st term is  {{{a[1]}}} = {{{a[5]*(1/2)^(-4)}}} = {{{2^4}}} = 16.


(b)  The n-th term is  {{{a[n]}}} = {{{a[1]*(1/2)^(n-1)}}} = {{{16/2^(n-1)}}} = {{{2^(5-n)}}} = {{{2^5/2^n}}} = {{{1/2^(n-5)}}}.    <U>ANSWER</U>


For (b), you can take any of these four last equivalent expressions.
</pre>

Solved.


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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.


Learn the subject from there.