Question

Which recursive sequence would produce the sequence 7, 33, 137, ...?

a. a₁=7 and aₙ=-2aₙ₋₁+5
b. a₁=7 and aₙ=4aₙ₋₁+5

Answer 1

b

Explanation:

using the recursive sequence

a

a₁ = 7 and
`a_(n)` = - 2
`a_(n-1)` + 4

a₁ = 7

a₂ = - 2 × a₁ + 4 = - 2 × 7 + 4 = - 14 + 4 = = - 10 ≠ 33

b

a₁ = 7 and
`a_(n)` = 4
`a_(n-1)` + 5

a₁ = 7

a₂ = 4 × a₁ + 5 = 4 × 7 + 5 = 28 + 5 = 33

a₃ = 4 × a₂ + 5 = 4 × 33 + 5 = 132 + 5 = 137

Thus option b, produces the sequence 7 , 33 , 137