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

I have no idea how to do this

Originally Posted by needhelpplease1

#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.

Originally Posted by needhelpplease1

#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} $

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

Originally Posted by mathemagister

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

wait, wouldn't it be $\displaystyle tn = 64(-1/4)^n$?

Originally Posted by needhelpplease1

wait, wouldn't it be $\displaystyle tn = 64(-1/4)^n$?

No, because then when n = 1, you wouldn't get 64.

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.

Hope everything is clarified

Mathemagister