1. ## Arithmetic series

Find the first four terms of the sequence defined by:
Un = 4Un-1, U1 = 2
I know the steps, but i dont know what U2, U3, and U4. I think i someone explained that to me i will be able to do it.

2. Originally Posted by milan
Find the first four terms of the sequence defined by:
Un = 4Un-1, U1 = 2
I know the steps, but i dont know what U2, U3, and U4. I think i someone explained that to me i will be able to do it.
Is it not something like

Un+1 = 4Un-1 ?

3. Nope, its exactly how i wrote it.

4. The way that is written then it is saying that $\displaystyle Un = 4Un-1$.

So $\displaystyle U1 = 4U1-1$
$\displaystyle 2 = 4x2 - 1$.

If the formula you have means that the next one in the squence is equal to $\displaystyle 4Un-1$

Then you would have $\displaystyle 2, (4x2)-1, (4x((4x2)-1)-1$.

Obviously you would simplify the above answer

5. Is not just
$\displaystyle \begin{gathered} u_1 = 2 \hfill \\ u_2 = 4u_1 = 8 \hfill \\ u_3 = 4u_2 = 32 \hfill \\ u_4 = 4u_3 = 128 \hfill \\ \end{gathered}$?

6. Originally Posted by Plato
Is not just
$\displaystyle \begin{gathered} u_1 = 2 \hfill \\ u_2 = 4u_1 = 8 \hfill \\ u_3 = 4u_2 = 32 \hfill \\ u_4 = 4u_3 = 128 \hfill \\ \end{gathered}$?
There is also a -1 after the 4Un.

I think the confusion is from the fact it normally says Un+1 = ...

Or the ones I have done in the past have, not sure about anyone else?

7. Oh, ok, i get it now, i was just a bit stupid haha.

8. Originally Posted by craig
The way that is written then it is saying that $\displaystyle Un = 4Un-1$.

So $\displaystyle U1 = 4U1-1$
$\displaystyle 2 = 4x2 - 1$.

If the formula you have means that the next one in the squence is equal to $\displaystyle 4Un-1$

Then you would have $\displaystyle 2, (4x2)-1, (4x((4x2)-1)-1$.

Obviously you would simplify the above answer
No. The OP means Un = 4U_(n-1) or, even better, $\displaystyle Un = 4U_{n-1}$.

You will need to better learn how to interpret poor formatting (which is why users are encouraged to learn basic latex).

To the OP:

Originally Posted by milan
[snip]
Un = 4Un-1, U1 = 2
[snip]
Originally Posted by milan
Nope, its exactly how i wrote it.
Nope, it's not exactly how you wrote it. Please take the time to learn some basic latex so that you can format equations more clearly next time. See here: http://www.mathhelpforum.com/math-help/latex-help/

9. Originally Posted by mr fantastic
No. The OP means Un = 4U_(n-1) or, even better, $\displaystyle Un = 4U_{n-1}$.
Don't know how you managed 2 work out that it was that lol

10. Originally Posted by craig
Don't know how you managed 2 work out that it was that lol
Eliminate what doesn't make sense and hopefully you're left with just one interpretation that does (although often that won't be the case, unfortunately).

11. Originally Posted by craig
Don't know how you managed 2 work out that it was that lol
The closed form is $\displaystyle u_n = 2^{2n-1}.$