1. ## Sequences

1) Determine whether each recursive formula defines an arithmetic sequence,if it is arithmetic state the first five terms
a) T^1=1, t^n =2t^n-1-n+2
how do we know if its arithmetic ? Pleasehelp

2. ## Re: Sequences

Originally Posted by darkangel06
a) T^1=1, t^n =2t^n-1-n+2
First, please explain how we are supposed to decide whether t^n-1-n+2 means tn-1-n+2, tn-1-n+2, tn-1-n+2 or tn-1-n+2. Second, you can calculate the first several terms of the sequence and make a hypothesis whether it is arithmetic. Then it can be proved.

3. ## Re: Sequences

I got that can you help me with this :
The 5th term of a geometric sequence is 45 and the 8th term is 360 determine the 20th term

4. ## Re: Sequences

Originally Posted by darkangel06
I got that can you help me with this :
The 5th term of a geometric sequence is 45 and the 8th term is 360 determine the 20th term
The nth term, $\displaystyle t_n$, of a geometric sequence, with first term a and common multiple r, is $\displaystyle t_n= ar^{n-1}$. Surely you knew that?

So the 5 term is $\displaystyle ar^4= 45$ and the 8th term is $\displaystyle ar^7= 360$. Use those to determine the values of a and r and the finnd $\displaystyle a_{20}= ar^{19}$.

5. ## Re: Sequences

Do i divide them ?

6. ## Re: Sequences

Originally Posted by darkangel06
Do i divide them ?
Don't worry: if you do, the paper won't burst into flames. In other words, why don't you try?

7. ## Re: Sequences

I dont get how to find a and r

8. ## Re: Sequences

ar7 = 360 and ar4 = 45. Divide the first equation by the second one, i.e., divide the left-hand sides and then the right-hand sides and equate the results. Alternatively, express a from the second equation: a = 45 / r4 and substitute it into the first equation.