Question

The sequence {an } is defined by a of o = 1 and a of n + 1 = 2 a of n + 2 for n = 0, 1, 2.... What is the value of a of 3?

Answer 1

`\begin{cases}a(0)=1\\a(n+1)=2a(n)+2&\text{for }n\ge0\end{cases}`

Use the second part of the definition (the recursive one):



`a(1)=2a(0)+2=4`

`a(2)=2a(1)+2=10`

`a(3)=2a(2)+2=22`