Understanding Binomial Coefficients: Finding the r-th term formula

[gschjetne]

I'm working on an IB mathematics portfolio, and here's a problem I don't understand:

The formula for the general term is
<br /> T_n+1=C_n^r a^{n-r} b^r<br />
Verify this formula by examples. This is the formula for the (r+1)-th term.
What would the formula for the r-th term be?

It's not specified what a and b is supposed to represent. That's where I need some explanation.
I already made a nice Pascal triangle all the way to the 10th row.
All help is appreciated.

 

[dextercioby]

My guess is that it comes from the expansion:

(a+b)^{n}=\sum_{k=0}^{n}C_{n}^{k} a^{n-k}b^{k}

Daniel.

PS.Can u handle the (n-1) term part??

 

[gschjetne]

Thanks, I'll give it a try