Question

What is the recursive formula for the geometric sequence 2, 12, 72, 432,.. ?

Answer 1

$a_{1}=2\\a_{n}=6a_{n-1}$

Answer 2

The recursive formula is  aₙ = 2(6)ⁿ⁻¹.

What is recursive formula?

A recursive formula for a geometric sequence with common ratio r is given by aₙ = a₁ rⁿ⁻¹ for n≥2.

Given: 2, 12, 72, 432,..

r= 12/2= 6

a= 2

The recursive  formula for the nth term,

aₙ = a₁ rⁿ⁻¹

aₙ = 2(6)ⁿ⁻¹

Hence, the recursive formula is aₙ = 2(6)ⁿ⁻¹

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