Math Help - Sequence Proof

1. Sequence Proof

i need to prove the following:

let:
a1 = 3
an+1 = (1/3)(an + 12)

for all n in N. show that the sequence an converges, and then find the limit

Thanks!

2. Originally Posted by dlee426
i need to prove the following:

let:
a1 = 3
an+1 = (1/3)(an + 12)

for all n in N. show that the sequence an converges, and then find the limit

Thanks!
You need to first show that the sequence is bounded from above [i.e. prove by induction that $a_k] and show that it is monotone [prove by induction that $s_{k}]. Once you've done that, note that as $n\to\infty$, $a_{n+1}\to a,\,a_{n}\to a$. Thus $a=\tfrac{1}{3}\left(a+12\right)\implies a=\dots$

Can you take it from here?
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