Question 1056796
(1)
General term is {{{A*r^(n-1)}}}.
{{{system(A*r^(2-1)=24,A*r^(5-1)=81)}}}
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{{{system(Ar=24,Ar^4=81)}}}


{{{(Ar^4)/(Ar)=81/24}}}


{{{r^3=(9*9)/(3*2*2*2)}}}


{{{r^3=27/(2*2*2)}}}


{{{r^3=(3^3)/(2^3)}}}


{{{r=3/2}}}


General Term more specifically is  {{{A(3/2)^(n-1)}}}.  You still need to know A, before you can find the term for any index n.


{{{A(3/2)=24}}}

{{{A=24(2/3)}}}

{{{A=16}}} and from this you know the general term is  {{{highlight(16(3/2)^(n-1))}}}.