Question

The numbers x-6, 2x and x square are in General. P. Find x and 1st term and nth term

Answer 1

Step-by-step explanation:

x - 6, 2x, x^2 are in GP

a1 = x - 6

a2 = 2x

a3 = x^2

common ratio

$\frac{a2}{a1} = \frac{a3}{a2} \\ \frac{2x}{x - 6} = \frac{ {x}^{2} }{2x} \\ \frac{2x}{x - 6} = \frac{x}{2} \\ 2(2x) = x(x - 6) \\ 4x = {x}^{2} - 6x \\ {x}^{2} - 6x - 4x = 0 \\ {x}^{2} - 10x = 0 \\ x(x - 10) = 0 \\ x = 0 \: \: \: \: or \: \: \: x - 10 = 0 \: \: \: \: x = 10$

x = 10

the GP is

x - 6 = 10 - 6 = 4

2x = 2 × 10 = 20

x^2 = 10^2 = 100

first term = 4

a = 4 r = 5

nth term

$a {r}^{n - 1} = 4 \times {5}^{n - 1}$

hope you get your answer