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):


$a(1)=2a(0)+2=4$
$a(2)=2a(1)+2=10$
$a(3)=2a(2)+2=22$