1. ## Binomial Theorem Chapter

I am taking Gr 12 Data Management online and am really struggling to understand this chapter. One of the questions is:

The first three terms in the expansion of (1+ay)^n are 1, 12y, and 68y^2. Evaluate a and n. Use the fact that

(1+ay)^n=1+nay+(n(n-1)/2)(ay)^2+...

I have gone over my notes and the text and dont know how go about evaluating for a and n. Any help would be greatly appreciated! Thanks in advance

2. Originally Posted by shell
I am taking Gr 12 Data Management online and am really struggling to understand this chapter. One of the questions is:

The first three terms in the expansion of (1+ay)^n are 1, 12y, and 68y^2. Evaluate a and n. Use the fact that

(1+ay)^n=1+nay+(n(n-1)/2)(ay)^2+...

I have gone over my notes and the text and dont know how go about evaluating for a and n. Any help would be greatly appreciated! Thanks in advance

So you have

$nay = 12 y$ and so $na = 12$,

and

$\frac{n(n-1)(ay)^2}{2} = 68y^2$ and so $\frac{n(n-1)a^2}{2} = 68$.

Giving you 2 equations in two unknowns, $na = 12$ gives $a=\frac{12}{n}$, substitute this into the second equation and solve for n.

Hope this helps.