Answer: T₇.
- A T₅
- B T₆
- C T₇
- D T₈
Correct answer: C. T₇
Explanation: |T(r+1)/Tr| = |(10-r+1)/r x (-3x/2)| = (11-r)/r x 3/2. Set >= 1: 3(11-r) >= 2r. 33-3r >= 2r. 33 >= 5r. r <= 6.6. Check r=6: T7/T6 = 5/6 x 3/2 = 15/12 > 1, so T7 > T6. Check r=7: T8/T7 = 4/7 x 3/2 = 12/14 < 1, so T8 < T7. So T7 is the greatest term.
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