# recurrence relation issues

• May 22nd 2007, 05:11 PM
pwr_hngry
recurrence relation issues
The solution to the recurrence relation a_n = a_n-1 + 3 with initial condition a0 = 2

The answer that I got was

an = 3 + lg 2n

I know that the answer will be similar to this in form I am just not feeling confident in the answer I came up with.

Thanks for taking a look.

pwr
• May 22nd 2007, 06:45 PM
topsquark
Quote:

Originally Posted by pwr_hngry
The solution to the recurrence relation a_n = a_n-1 + 3 with initial condition a0 = 2

The answer that I got was

an = 3 + lg 2n

I know that the answer will be similar to this in form I am just not feeling confident in the answer I came up with.

Thanks for taking a look.

pwr

Well,
$\displaystyle a_0 = 2$
$\displaystyle a_0 = 3 + lg(2 \cdot 0) \to \infty$
(I presume "lg" is a logarithm function to some base?)

Let's take a look at the sequence.
$\displaystyle a_0 = 2$
$\displaystyle a_1 = a_0 + 3 = 2 + 3 = 5$
$\displaystyle a_2 = a_1 + 3 = 5 + 3 = 8$
$\displaystyle a_3 = a_2 + 3 = 8 + 3 = 11$
etc.

So it looks like:
$\displaystyle a_n = a_0 + 3n = 3n + 2$

-Dan