1) - 1/2 , 1/4 , - 1/2 , 1/4

2) 11, 8, 13, 6, 15,...

3) 8,4,8,4,8,4,...

and could you guys share any tips on how to quickly find the nth term.

any help is much appreciated. thank you :)

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- Jul 14th 2012, 06:53 PMnisbahmumtazFinding the nth term of the following sequence
1) - 1/2 , 1/4 , - 1/2 , 1/4

2) 11, 8, 13, 6, 15,...

3) 8,4,8,4,8,4,...

and could you guys share any tips on how to quickly find the nth term.

any help is much appreciated. thank you :) - Jul 14th 2012, 07:34 PMSorobanRe: Finding the nth term of the following sequence
Hello, nisbahmumtaz!

(1) and (3) are oscillating sequences.

There are several ways to express the general term.

I'll show you one of them.

Quote:

. . I call it the "blinker" function.

Quote:

This sequence oscillates between 8 and 4.

The general term is: .

- Jul 14th 2012, 07:52 PMHallsofIvyRe: Finding the nth term of the following sequence
It's pretty obvious isn't it? Assuming the indexing starts at 1, is -1/2 if n is odd, 1/4 if no is even. If you want a single "formula" note that is -1 if n is odd and 1 if n is even. And that [itex]\frac{3}{8}- (-1)^n\frac{1}{8}[/tex] is if n is odd, if n is even.

Quote:

2) 11, 8, 13, 6, 15,...

Quote:

3) 8,4,8,4,8,4,...

Quote:

and could you guys share any tips on how to quickly find the nth term.

any help is much appreciated. thank you :)

- Jul 15th 2012, 09:56 AMSorobanRe: Finding the nth term of the following sequence
Hello again, nisbahmumtaz!

The second one is tricky . . .

Quote:

Look at the differences of consecutive terms.

. .

Each term is: the previous term plus/minus a consecutive odd number.

We can write a recursive relation like this: .

Maybe someone can come up with a closed form?

- Jul 15th 2012, 10:42 AMa tutorRe: Finding the nth term of the following sequence
- Jul 19th 2012, 01:08 AMa tutorRe: Finding the nth term of the following sequence
So as well as the simple we can also have which produces the sequence 11,8,13,6,15,116,433....