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.
\(\frac{-1}{2}, 8\)
\(\frac{1}{2}, -8\)
\(\frac{-1}{2}, -8\)
\(\frac{1}{2}, 8\)
Correct answer is A
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 = (\(\frac{-1}{2}, 8\))