34. 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 + ...
Any help in evaluating 'a' and 'n' would be GREATLY appreciated!
34. 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 + ...
Any help in evaluating 'a' and 'n' would be GREATLY appreciated!
Coefficient of y: $\displaystyle 12 = na$ .... (1)
Coefficient of $\displaystyle y^2$: $\displaystyle \frac{n(n-1)}{2} \, a^2 = 68 \Rightarrow n(n-1) a^2 = 136$ .... (2)
Now solve equations (1) and (2) simultaneously. Hint: Note that when you square equation (1) you get $\displaystyle 144 = n^2 a^2$.