Theory question 101
Binomial Theorem(a) If the coefficient of x2 and x3 in the expansion of (p + qx)7 are equal, express q in terms of p.
(b) A man makes a weekly contribution into a fund. In the first week, he paid ₦180.00, second week ₦260.00, third week ₦340.00 and so on. How much would he have contributed in 16 weeks?
Show the model answer
Model answer
(a) Coefficient of x² = ⁷C₂p⁵q² = 21p⁵q²; of x³ = ⁷C₃p⁴q³ = 35p⁴q³.
21p⁵q² = 35p⁴q³ gives q = 21p/35 = (3/5)p.
(b) A.P. with a = 180, d = 80, n = 16.
S₁₆ = (16/2)[2(180) + 15(80)] = 8 × 1560 = ₦12,480.00.
Explanation
The general term of (p + qx)ⁿ is ⁿCᵣ pⁿ⁻ʳ(qx)ʳ.