Question 945179
{{{b[1]=3&5/9=32/9}}} is the first term of a geometric sequence with {{{7}}} terms with common ratio {{{r}}} .
{{{b[7]=b[1]*r^6=40&1/2=81/2}}} is the last and seventh term of that same sequence.
{{{B[7]/b[1]=r^6=((81/2))/((32/9))=(81/2)*(9/32)=(3^4/2)*(3^2/2^5)=(3^4*3^2)/(2*2^5)=3^6/2^6=(3/2)^6}}} .
So, {{{system(r=3/2,"or",r=-3/2)}}} .
Either way, the fifth term is
{{{b[5]=b[1]*r^4=(32/9)*(3/2)^4=(2^5/3^2)*(3^4/2^4)=(2^5*3^4)/(3^2*2^4)=2^((5-4))*3^((4-2))=2^1*3^2=2*9=highlight(18)}}} .