Thread: 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!

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 ] and show that it is monotone [prove by induction that ]. Once you've done that, note that as , . Thus

Can you take it from here?