# Sequences

• May 27th 2013, 12:55 PM
darkangel06
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
• May 27th 2013, 01:01 PM
emakarov
Re: Sequences
Quote:

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.
• May 27th 2013, 01:37 PM
darkangel06
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
• May 27th 2013, 01:47 PM
HallsofIvy
Re: Sequences
Quote:

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}\$.
• May 27th 2013, 01:56 PM
darkangel06
Re: Sequences
Do i divide them ?
• May 27th 2013, 02:03 PM
emakarov
Re: Sequences
Quote:

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?
• May 27th 2013, 02:20 PM
darkangel06
Re: Sequences
I dont get how to find a and r
• May 27th 2013, 02:35 PM
emakarov
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.