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.

  • A \(\frac{-1}{2}, 8\)
  • B \(\frac{1}{2}, -8\)
  • C \(\frac{-1}{2}, -8\)
  • D \(\frac{1}{2}, 8\)
waec 2022furthermathematics

The correct answer is A. \(\frac{-1}{2}, 8\)

U1 = x - 4

U2 = x + 2

U3 = 3x + 1

\(\frac{u_2}{u_1} = \frac{u_3}{u_2}\)

\(\frac{x+2}{x-4} = \frac{3x+1}{x+2}\)

(x+2)(x+2) = (x-4)(3x+1)

x\(^2\) + 4x + 4 = 3x2 - 11x - 4

collecting like terms

2x\(^2\) - 15x - 8 =0

2x\(^2\) + x - 16x - 8 = 0

x(2x + 1) - 8(2x + 1) = 0

(x-8)(2x+1) = 0

x = (\(\frac{-1}{2}, 8\))

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