The first term of a GP is 1 . The sum of the third and fifth term is 90 , then common ratio $=$ $\_\

Question

The first term of a GP is 1 . The sum of the third and fifth term is 90 , then common ratio $=$ $\_\_\_\_$

Professor PC Thomas Classes · Answer

$ar^2 + ar^4 = 90 \implies r^2 + r^4 = 90 \implies r^4 + r^2 - 90 = 0 \implies (r^2+10)(r^2-9) = 0 \implies r^2=9 \implies r=\pm 3$.