Geometric Series ?

Question

Find a_10 if a_3=135 and r=1/3

Answer 1

a₁₀ = a₃(r⁷)

a₁₀ = 135(1/3)⁷

a₁₀ = 5(3³)(1/3⁷)

a₁₀ = 5 / 3⁴

a₁₀ = 5 / 81

Answer 2

a(n) = a(1) * r^(n-1)

Here a(1) is a_3, r = 1/3 and n-1 = 8-1 = 7 (a(3) through a(10) is 8 numbers)

a_10 = a_3 * 1/3^7 = 135 /2187 = 45/729 = 15/243 = 5/81