Question

Given the recursive sequence defined by:

tn=5tn-1 + 3tn-2
with ti=2 and t2 = 4
Which of the following would be the first 5 terms of the sequence?

Answer 1

2, 4, 26, 142, 788

Explanation:

Using the recursive rule and t₁ = 2, t₂ = 4 , then

t₃ = 5t₂ + 3t₁ = 5(4) + 3(2) = 20 + 6 = 26

t₄ = 5t₃ + 3t₂ = 5(26) + 3(4) = 130 + 12 = 142

t₅ = 5t₄ + 3t₃ = 5(142) + 3(26) = 710 + 78 = 788

First 5 terms are 2, 4, 26, 142, 788