How do I find the General Term of a Sequence?

[XEROX_FAN]

1. Write down the general term of each of the following sequences in simplest form:
So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ...

I really need to find an equation that I can use to determine the general term for any given sequence.

Homework Equations

?[/B] Umm trying to find one ...

The Attempt at a Solution

:[/B] tn = -n
and that's about as far as I got ...

 

[STEMucator]

1. Write down the general term of each of the following sequences in simplest form:
So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ...

I really need to find an equation that I can use to determine the general term for any given sequence.2. Homework Equations ? Umm trying to find one ...
3. The Attempt at a Solution : tn = -n
and that's about as far as I got ...

There really is no general formula to find the general term of a sequence. You essentially have to look for a pattern in the numbers.

Notice the terms in your sequence are alternating positive and negative. This tells you $(-1)^n$ will be part of the general term. What else do you notice?