WAEC 2022 · Paper 1 · Q26

The first, second and third terms of an exponential sequence (G.P.) are $(x - 4)$ , $(x + 2)$ and $(3x + 1)$ respectively. Find the values of $x$ .

Worked solution (try it first)

In a G.P. the common ratio is the same, so $\dfrac{x + 2}{x - 4} = \dfrac{3x + 1}{x + 2}$ , giving $(x + 2)^2 = (x - 4)(3x + 1)$ .
Expand: $x^2 + 4x + 4 = 3x^2 - 11x - 4$ , so $2x^2 - 15x - 8 = 0$ .
Factorise: $(2x + 1)(x - 8) = 0$ .
So $x = -\frac12$ or $x = 8$ , option A.