Question

A1 = 5
an = an-1 (3)
what is the 3rd term of this sequence?

Answer 1

45

Explanation:

If a(1) = 5, then a(2) = a(1)*3, or 5*3, or 15.

If a(2) = 15, then a(3) = a(2)*3, or a(3) = 15*3 = 45

This is a geometric sequence with first term a(1) = 5 and common ratio 3. We can immediately write the explicit formula

a(n) = 5*3^(n - 1), which correctly predicts that a(3) = 5*3^(3 - 1) = 5*9 = 45