Question

This recursive formula represents a geometric sequence: a1 = 2 an = 6(an − 1); for n ≥ 2 Select the geometric sequence that can be constructed from the given recursive formula, and select the explicit formula for the sequence.

Answer 1

A & D

Explanation:

{2, 12, 72, 432, 2,592, . . .}

an = 2(6)n − 1

Answer 2

f(n)=2X6ⁿ⁻¹

Explanation:

a₁=2

aₙ=6aₙ₋₁ for n≥2

a₂=6a₂₋₁=6a₁=6*2=12

a₃=6a₃₋₁=6a₂=6*12=72

a₄=6a₄₋₁=6a₃=6*72=432

This is a geometric sequence with:

First term, a=2

Common ratio, r= 12/2=6

For a geometric sequence, the nth term is given by:

Uₙ=arⁿ⁻¹

Uₙ=2X6ⁿ⁻¹

Therefore, the explicit formula for the sequence f(n) is given as:

f(n)=2X6ⁿ⁻¹