Question

A recursively defined is shown below

Answer 1

Answer:

a₄ = -9

Step-by-step explanation:

Given:

a₁ = 5

aₙ₊₁ = 2aₙ - 7

To calculate a₄ we would use 3 for n.

aₙ₊₁ = 2aₙ - 7

a₃₊₁ = 2a₃ - 7

a₄ = 2a₃ - 7

However we don't know a₃. Let's start from the bottom.

a₁ = 5

a₂ = a₁₊₁ = 2a₁ - 7

             = 2(5) - 7

             = 10 - 7

             = 3

a₃ = a₂₊₁ = 2a₂ - 7

             = 2(3) - 7

             = 6 - 7

             = -1

a₄ = a₃₊₁ = 2a₃ - 7

             = 2(-1) - 7

             = -2 - 7

             = -9