Question

Given the following system of equations for n≥2, find a5.

a1=2

an=3⋅an−1−1

Select one:
a. 41
b. 122
c. 365
d. 2,094

Answer 1

b

Explanation:

using the recursive rule
`a_(n)` = 3
`a_(n-1)` - 1 and a₁ = 2 , then

a₂ = 3a₁ - 1 = (3 × 2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = (3 × 5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = (3 × 14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = (3 × 41) - 1 = 123 - 1 = 122