Answer: 55.
- A 45
- B 46
- C 56
- D 55
Correct answer: D. 55
Explanation: T8 = nC7 (2)n-7 (x/3)7 and T9 = nC8 (2)n-8 (x/3)8. Equal coefficients: nC7/nC8 = 2/3. Since nC8/nC7 = (n-7)/8, we get (n-7)/8 = 3/2. n-7 = 12. n = 55.
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