how to determine the general term

**needhelpplease1** · Apr 8th 2010, 10:40 AM

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

I have no idea how to do this

**mathemagister** · Apr 8th 2010, 10:53 AM

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.

**harish21** · Apr 8th 2010, 10:54 AM

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

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

Note: This is the recurrence relation.

The series is expressed as what mathemagister has stated:

${a_n} = [-(-1)^n] 4^{4-n}$

**mathemagister** · Apr 8th 2010, 10:58 AM

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

**needhelpplease1** · Apr 8th 2010, 11:07 AM

Originally Posted by mathemagister

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

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

**mathemagister** · Apr 8th 2010, 11:11 AM

Originally Posted by needhelpplease1

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

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

EDIT: I think you were thinking of $t_n = 64(-1/4)^{n-1}$ which is also a correct way to express the sequence.

Hope everything is clarified

Mathemagister

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how to determine the general term

hmm..

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