WAEC 2018 · Paper 2 · Q3

(a)
The sum of the second and third terms of a Geometric Progression (G.P.) is 48. If the sum of the third and fourth terms is 144, find the first term of the progression.

Worked solution (try it first)

The second and third terms: $ar + ar^2 = 48$ , which factorises to $ar(1 + r) = 48$ .
The third and fourth terms: $ar^2 + ar^3 = 144$ , which factorises to $ar^2(1 + r) = 144$ .
Divide the second equation by the first: $r = \dfrac{144}{48} = 3$ .
Substitute: $a(3)(4) = 48$ , so the first term is $a = 4$ .