Algebraic Expression: Pattern for Term t

[Natko]

Homework Statement

In this pattern, what is the algebraic expression for the term t?
-15, 30, 90, -360

Homework Equations

t= term number

The Attempt at a Solution

no idea

 

[DivisionByZro]

What do you multiply each term by to get the next?

 

[Natko]

What do you multiply each term by to get the next?

That's what I want to find out. It does not necessarily have to be multiplication only.

In words it would be:
current term value = the previous term's value multiplied by the current term number, and change poles if the current term number is even; the first term value is -15.

 

[HallsofIvy]

Are you saying that you have a sequence, a_1= -15, a_2= 30, a_3= 90, and a_4= -360?

Well, I notice that 30= 2*15, 90= 3*30, and 360= 4*90. That is, a_n= n*a_{n-1}. Also, the signs are -, +, +, -. You should be able to find a power of -1, in terms of n, that will give that.

 

[Natko]

Are you saying that you have a sequence, a_1= -15, a_2= 30, a_3= 90, and a_4= -360?

Well, I notice that 30= 2*15, 90= 3*30, and 360= 4*90. That is, a_n= n*a_{n-1}. Also, the signs are -, +, +, -. You should be able to find a power of -1, in terms of n, that will give that.

So what would the algebraic expression to find the n^th term be?