Question

1. Write a recursive definition
2. Write an explicit formula

Answer 1

1. a₁ = 14, aₙ = aₙ₋₁ - 4

2. aₙ= -13 + 7(n - 1)

Explanation:

1. Recursive definition

a₁ = 14

a₂ = 10

a₃ = 6

a₄ = 2

Each term (aₙ) is four units less than the preceding term (aₙ₋₁)

The recursive definition is

a₁ = 14, aₙ = aₙ₋₁ - 4

2. Explicit formula

a₁ = -13

a₂ = -6

a₃ = 1

a₄ = 8

Each term (aₙ) is seven units more than the preceding term (aₙ₋₁)

The explicit formula is

aₙ= -13 + 7(n - 1)