Question

11. Given that ⁸Cₓ, ⁷Cₓ, and 7/6(⁶Cₓ) form the first three consecutive terms of an exponential sequence (G.P.), find: (a) the value of x; (b) the common ratio of the sequence; (c) the sum of the first ten terms of the sequence.

Accepted Answer

(a) Setting up the G.P. condition (⁷Cₓ)² = ⁸Cₓ × (7/6)⁶Cₓ and simplifying the factorial ratios leads to x=4.
(b) With x=4: ⁸C₄=70, ⁷C₄=35, and 7/6(⁶C₄)=7/6(15)=35/2. So u1=70, u2=35, u3=35/2, giving common ratio r=1/2.
(c) Sum of first 10 terms: S₁₀ = a(1-r¹⁰)/(1-r) = 70(1-1/1024)/(1/2) = 70(1023/1024)×2 = 35805/256.

WAEC Further Mathematics 2025 Theory — Question 11

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