Question 1207190
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The first term of a geometric sequence is 2, and the 4th term is 250. 
Find the 2 terms between the first and the 4th term.
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<pre>
    {{{a[1]}}} = 2,

    {{{a[4]}}} = {{{a[1]*r^3}}} = 250.


Hence,  

    {{{2*r^3}}} = 250

     {{{r^3}}} = 250/2 = 125

      r = {{{root(3,125)}}} = 5.


The two terms between the first and the 4th terms are

    {{{a[2]}}} = {{{r*a[1]}}} = 5*2 = 10,

     {{{a[3]}}} = {{{r*a[2]}}} = 5*10 = 50.
</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.