Question Detail
Question
In the expansion of (1 + rx)ⁿ, the first three terms are 1 - 10x + 40x². Find n + r.
Correct Answer
Option B is the correct answer.
Detailed Explanation
First three terms: 1 + n(rx) + n(n-1)/2 (rx)² = 1 + nr x + [n(n-1)r²/2] x². Given: nr = -10, and n(n-1)r²/2 = 40. From nr = -10, r = -10/n. Substitute: n(n-1)(100/n²)/2 = 40 ⇒ (n-1)(100/n)/2 = 40 ⇒ 100(n-1)/(2n) = 40 ⇒ 50(n-1)/n = 40 ⇒ 50n - 50 = 40n ⇒ 10n = 50 ⇒ n = 5. Then r = -10/5 = -2. So n + r = 5 + (-2) = 3.
Hint
Use the binomial expansion and equate coefficients.