Geometric sequence nth term

Question

Sequence 9, 36/5, 144/25

What is the nth term?

Thank you

Answer 1

With a geometric sequence, the terms have a common ratio.

This sequence starts with n₁ and has a common ratio of:

a₂ / a₁ = (36/5) / 9 = 4/5

a₃ / a₂ = (144/25) / (36/5) = (144/25) * (5/36) = 4/5

Note that the first element in the sequence is n₁.

The n^th element is found using the formula:

a_n = a₁r^n-1

Here, a₁ = 9

r = 4/5

The n^th term is found by evaluating:

a_n = 9*(4/5)^n-1