Question

11(a). The third and sixth terms of a Geometric Progression (G.P.) are 1/4 and 1/32 respectively. Find:
(i) the first term and common ratio;
(ii) the seventh term.
(b) Given that 2 and −3 are the roots of the equation ax²+bx+c=0, find the values of a, b and c.

Accepted Answer

(a) nth term of a G.P. = arⁿ⁻¹. Third term (n=3): ar² = 1/4 …(i). Sixth term (n=6): ar⁵ = 1/32 …(ii). Dividing (ii) by (i): r³ = (1/32)/(1/4) = 1/8 ⇒ r = ½. From (i): a(½)² = 1/4 ⇒ a(1/4)=1/4 ⇒ a = 1.
(i) First term a = 1, common ratio r = ½.
(ii) Seventh term (n=7): ar⁶ = 1×(½)⁶ = 1/64.

(b) If the roots are 2 and −3: sum of roots = 2+(−3) = −1; product of roots = 2×(−3) = −6. The equation is x²−(sum of roots)x+(product of roots)=0 ⇒ x²−(−1)x+(−6)=0 ⇒ x²+x−6=0. Comparing with ax²+bx+c=0: a=1, b=1, c=−6.

WAEC Mathematics 2019 Theory — Question 13

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