The term in a certain geometric sequence is 16 and the term in the sequence is 24. What is the term?

A formula for the n^th term of a geometric sequence is:  t_n  =  a · r^{n - 1}.

--->   16  =  a · r²² 

--->   24  =  a · r²⁷

Dividing the top equation by the bottom equation (and cancelling out the a's):  16/24  =  r²² / r²⁷

--->  2/3  =  r^-5     --->   3/2  =  r⁵     --->   r  =  (3/2)^1/5     (which is the fifth root of 3/2)

Since  16  =  a · r²²      --->   16  =  a · ( (3/2)^1/5 )²²    --->   a  =  16 / ( (3/2)^1/5 )²²  

To find the 43rd term:  a · r^{n - 1}     --->    16 / ( (3/2)^1/5 )²² · ( (3/2)^1/5 )⁴²    --->   16 · (3/2)⁴