Question

Express the terms of the following geometric sequence recursively 3,6,12,24,4&

Answer 1

aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3

Explanation:

A geometric sequence can be expressed recursively using the following general equation

aₙ = r . (aₙ₋₁), n ≥ 2
where
aₙ is the nth term
a₁ is the first term of the geometric sequence

r is the common ratio = aₙ/aₙ₋₁

Here we have the terms 3, 6, 12, 24, 48

The common ratio r = 6/3 = 12/6 = ....... = 48/24 = 2

The first term a₁ = 3

So the recursive relation is
aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3