Question 1038972
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For a given geometric sequence, the 5th term, a5, is equal to 11/256, and the 10th term, a10, is equal to 44. 
Find the value of the 12th term, a12. If applicable, write your answer as a fraction. 
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Take the ratio {{{a[10]/a[5]}}} = {{{44/((11/256))}}} = {{{256*4}}} = 1024 = {{{2^10}}}.


Take the 5-degree root of this ratio: {{{root(5, 2^10)}}} = {{{2^2}}} = 4.


It is your {{{r}}}, the common ratio.


Then multiply {{{a[10]}}} by {{{r^2}}}.


You will get {{{44*4^2}}} = {{{704}}}.


It is your answer.


As the last step, think, why it is correct.


Your lesson on geometric progressions is <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A> in this site.