Question

Write an explicit rule for the general term of the sequence 5, 15, 45,...?

Answer 1

a_n = 5 × 3^(n - 1)

Explanation:

The first term is 5. Each subsequent term is the previous term multiplied by 3.

a_1 = 5 × 3^0

a_2 = 15 = 5 × 3^1

a_3 = 45 = 5 × 3²

Notice that the exponent of the 3 is 1 less then the term number.

a_n = 5 × 3^(n - 1)