Question

The first term of a geometric sequence is 6, and the third term is 25/6. find the fifth term.

Answer 1

geo : a(n) = a(1)r^(n-1)
first term = 6 = a(1)

3rd term.
a(3) = 25/6
a(1)r^(3-1) = 25/6
6r^2 = 25/6
r = 5/6

so a(n) = 6(5/6)^(n-1))
a(5) = 6(5/6)^(5-1)) = 5^4/6^3