Thread: Proof by induction

So, I do this at sixth form, but in further maths, so I guess it's closer to Uni maths than 'pre-college' work.

I'm really stuck, I can't even work out my base step for this proof properly!

Prove that the general term of the sequence described by
U(n+1) = 3U(n) + 4, n E Z+
is U(n) = 3^n - 2 n E Z+

where u(1) = 1

Normally, on the divisibility and series ones we've done, the base step is n=1, but I can't see how that's going to help me with this?!

Originally Posted by thatsphatt

So, I do this at sixth form, but in further maths, so I guess it's closer to Uni maths than 'pre-college' work.

I'm really stuck, I can't even work out my base step for this proof properly!

Prove that the general term of the sequence described by
U(n+1) = 3U(n) + 4, n E Z+
is U(n) = 3^n - 2 n E Z+

where u(1) = 1

Normally, on the divisibility and series ones we've done, the base step is n=1, but I can't see how that's going to help me with this?!

Hi thatsphatt,

it seems that U(1)=1 is a missing piece of information.

Then, using











and so on...

Therefore

F(k)



F(k+1)





This means the formulation being true for n=1 causes the formulation to be true for n=2,
causing true for n=3, causing....... an infinite chain of cause and effect.

Test for n=1





Therefore, the nth term, in terms of n only is

Oh I see!
I think I'll be able to write down what I need from that!
Thank you