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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?

**Solution:**

It is given that

a_{0} = 1

a _{(n+1)} = 2a_{n} +2

Substitute n = 0

a _{(0 + 1) }= 2a_{0} + 2

a_{1} = 2 × 1 + 2

a_{1} = 2 + 2

a_{1} = 4

Substitute n = 1

a_{ (1 + 1)} = 2a_{1} + 2

a_{2} = 2 × 4 + 2

a_{2 }= 8 + 2

a_{2} = 10

Substitute n = 2

a_{ (2 + 1)} = 2a_{2} + 2

a_{3} = 2 × 10 + 2

a_{3} = 20 + 2

a_{3} = 22

Therefore, the value of a_{3} is 22.

## 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 a_{0} = 1 and a_{ (n+1)} = 2a_{n} +2 for n = 0,1,2.... the value of a_{3} is 22.

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