SOLUTION: 34. The first three terms in the expansion of (1+ay)^n are 1, 12y, and 68y^2 Evaluate a & n. Use the fact that (1 + ay)n = 1 + nay + n(n-1)/2 (ay)2 + _ _ _

Algebra ->  Exponents -> SOLUTION: 34. The first three terms in the expansion of (1+ay)^n are 1, 12y, and 68y^2 Evaluate a & n. Use the fact that (1 + ay)n = 1 + nay + n(n-1)/2 (ay)2 + _ _ _       Log On


   



Question 144476: 34. The first three terms in the expansion of (1+ay)^n are 1, 12y, and
68y^2
Evaluate a & n. Use the fact that
(1 + ay)n = 1 + nay + n(n-1)/2 (ay)2 + _ _ _

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The first three terms in the expansion of %281%2Bay%29%5En are 1, 12y, and 68y%5E2
the fact is that

%281-ay%29%5En+=+1-nay%2B+%28n%28n-1%29%2F2%29+%28ay%29%5E2+%2B+...
Compare coefficients,
-na+=+12......(1)
%281%2F2%29n%28n-1%29a%5E2+=+68......(2)
From (2), we have
n%5E2a%5E2+-+na%5E2+=+136......(3)
Plug in -na=12 in (3):
12%5E2-12%5E2%2Fn+=+136
Solve for n:
n+=+18
Solve for a:
a+=+-12%2F18+=+-2%2F3
Check:
%281%2B%282%2F3%29y%29%5E18
= 1+%2B+C%2818%2C1%29%282%2F3%29y+%2B+C%2818%2C2%29%282%2F3%29%5E2y%5E2+%2B+...