The sequence (an) is defined by a0 = 1 and a (n+1)= 2an +2 for n = 0,1,2.... what is the value of a3?

Solution:

It is given that

a₀ = 1

a _(n+1) = 2a_n +2

Substitute n = 0

a _{(0 + 1)} = 2a₀ + 2

a₁ = 2 × 1 + 2

a₁ = 2 + 2

a₁ = 4

Substitute n = 1

a _{(1 + 1)} = 2a₁ + 2

a₂ = 2 × 4 + 2

a₂ = 8 + 2

a₂ = 10

Substitute n = 2

a _{(2 + 1)} = 2a₂ + 2

a₃ = 2 × 10 + 2

a₃ = 20 + 2

a₃ = 22

Therefore, the value of a₃ is 22.

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The sequence (an) is defined by a0 = 1 and a (n+1) = 2an +2 for n=0,1,2.... what is the value of a3?

Summary:

The sequence (a_n) is defined by a₀ = 1 and a _(n+1) = 2a_n +2 for n = 0,1,2.... the value of a₃ is 22.