# how to determine the general term

• Apr 8th 2010, 10:40 AM
how to determine the general term
#1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

I have no idea how to do this :(
• Apr 8th 2010, 10:53 AM
mathemagister
Quote:

#1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

I have no idea how to do this :(

Here's a clue: notice how each term is -1/4 times the previous term. This, and your notes, should help you find the answer.
• Apr 8th 2010, 10:54 AM
harish21
Quote:

#1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

I have no idea how to do this :(

$\displaystyle a_{n+1} = \frac{-a_n}{4}$

Note: This is the recurrence relation.

The series is expressed as what mathemagister has stated:

$\displaystyle {a_n} = [-(-1)^n] 4^{4-n}$
• Apr 8th 2010, 10:58 AM
mathemagister
And that translates to $\displaystyle a_n = -(-1)^n 4^{4-n}$
• Apr 8th 2010, 11:07 AM
hmm..
Quote:

Originally Posted by mathemagister
And that translates to $\displaystyle a_n = -(-1)^n 4^{4-n}$

wait, wouldn't it be $\displaystyle tn = 64(-1/4)^n$?
• Apr 8th 2010, 11:11 AM
mathemagister
Quote:

wait, wouldn't it be $\displaystyle tn = 64(-1/4)^n$?
EDIT: I think you were thinking of $\displaystyle t_n = 64(-1/4)^{n-1}$ which is also a correct way to express the sequence.