Answer: a=2, n=3.
- A a=2, n=3
- B a=1, n=6
- C a=3, n=2
- D a=2, n=4
Correct answer: A. a=2, n=3
Explanation: Coefficient of x: na = 6. Coefficient of x²: n(n-1)a²/2 = 12. From na=6, a=6/n. Substituting: n(n-1)(36/n²)/2=12, so 18(n-1)/n=12, giving 18n-18=12n, 6n=18, n=3, a=2.
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term