Zaymiey

📐 Mathematics  ·  Binomial Theorem  ·  JEE

Find the middle term in (x/3 + 9y)⁸.

Answer: T₅.

  • A T₄
  • B T₆
  • C T₇
  • D T₅

Correct answer: D. T₅

Explanation: n=8 (even). Middle term = T(8/2+1) = T<sub>5</sub>.

Pascal's Triangle: Binomial Coefficients11112113311464115101051n=0n=1n=2n=3n=4n=5Each entry = sum of the two entries diagonally above it (Pascal's identity); row n gives nC0...nCn

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

Read the full Binomial Theorem notes →