Question

What is the value of the fourth term in a geometric sequence for which a1 = 15 and r = 1/3?

Express your answer as a fraction.

Answer 1

`a_1=15;\ r=(1)/(3)\\\\a_n=a_1r^(n-1)\to a_n=15\cdot\left((1)/(3)\right)^(n-1)\\\\a_4=15\cdot\left((1)/(3)\right)^(4-1)=15\cdot\left((1)/(3)\right)^3=15\cdot(1)/(27)=(15)/(27)=(5)/(9)\\\\\\Answer:\boxed{a_4=(5)/(9)}`