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

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- May 27th 2013, 12:55 PMdarkangel06Sequences
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 - May 27th 2013, 01:01 PMemakarovRe: Sequences
First, please explain how we are supposed to decide whether t^n-1-n+2 means t

^{n}-1-n+2, t^{n-1}-n+2, t^{n-1-n}+2 or t^{n-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. - May 27th 2013, 01:37 PMdarkangel06Re: 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 - May 27th 2013, 01:47 PMHallsofIvyRe: Sequences
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 $\displaystyle a_{20}= ar^{19}$. - May 27th 2013, 01:56 PMdarkangel06Re: Sequences
Do i divide them ?

- May 27th 2013, 02:03 PMemakarovRe: Sequences
Don't worry: if you do, the paper won't burst into flames. In other words, why don't you try?

- May 27th 2013, 02:20 PMdarkangel06Re: Sequences
I dont get how to find a and r

- May 27th 2013, 02:35 PMemakarovRe: Sequences
*ar*^{7}= 360 and*ar*^{4}= 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 /*r*^{4}and substitute it into the first equation.