# Help with mathematical induction

• Mar 22nd 2011, 07:44 AM
mechaniac
Help with mathematical induction
I have a series: $a_{0},a_{1},a_{2}...$

$a_{0}=1$
$a_{n+1}=\frac{((a_{n})^{2}+9)}{6}\hspace{6} n\geq 1$

i want to find a explicit form for $a_{n}$
and prove it with induction.

i calculated some values to use:
$a_{1}=\frac{5}{3}$
$a_{2}=\frac{53}{27}
$

i tried something like this:
$a_{n}=\frac{3n^4+n^2+1}{?}$

but im having a hard time finding a dominator that works with my values.

Maybe i´m doing it all wrong :)

regards mechaniac
• Mar 22nd 2011, 08:38 AM
Sambit
What do you mean by "explicit form"? If you want to get that expression in terms of $n$ only, you may not get one. You already have a recursive relation between $a_n$ and $a_{n+1}$; and this may be the most general form of the sequence.