Single correct · +4 / −1

If the expansion of (a + b)ⁿ has 13 terms, then n =

  1. (a) 6
  2. (b) 12
  3. (c) 13
  4. (d) 7
Answer and solution

Answer (b) 12

Solution

Maths sir · 3 steps

Terms are numbered by r from 0 to n, so there is always one more term than the power.

  1. Count the terms. The general term is Tᵣ₊₁ = C(n, r) aⁿ⁻ʳ bʳ, and r takes every whole value from 0 to n. That gives n + 1 terms in all.

    n + 1 = 13

  2. Quick check. For (a+b)² = a² + 2ab + b², the power is 2 and there are 3 terms. One more term than the power, every time.
  3. So. n = 13 - 1 = 12, which is option (b).

The idea to keep. In (a+b)ⁿ the count of terms is n+1, because r starts at 0, not 1. Always add one to the power when you count terms.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Binomial Theorem

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