Question

Find the 8th term of the geometric sequence if a3=108 and a5=972?

A. 2,268
B. 8,748
C. 26,244
D. 78,732

Answer 1

`a_3=a_1r^2=108`

`a_5=a_1r^4=972`


`\implies(a_5)/(a_3)=(a_1r^4)/(a_1r^2)\iff(972)/(108)=r^2\implies r=\pm\sqrt9=\pm3`


`a_8=a_1r^7=a_5r^3=972(\pm3)^3`

Judging by the given choices, the common ratio is likely the positive candidate, so


`a_8=972(3)^3=26244`

so the answer is C.