Question

15) The numbers x - 6, 2x and x? are in G.P. Find
(i) x (ii) 1st term (iii) nth term.​

Answer 1

Answer:

x = 0 ; x = -2 (2) -6 ; -8 (3) 0 ; - 2^ (3-n).

Step-by-step explanation:

(1)

x-6, 2x , x are in GP

So, (2x)^2 = (x-6)(x)

4x^2 = x^2 -6x

3x^2 + 6x = 0

x ( 3x + 6) = 0

x = 0 ; x = -2

(2)

1st term = x-6 = 0-6 = -6 or -2-6 = -8

(3) if x= 0 :

nth term = a r^n

= (-6) (0) ^n = 0

if x = -2 :

nth term = (-8) (1/2) ^n = -2^3 * 2 ^ (-n) = - 2^ (3-n).

Answer 2

Answer:

x = 10

First Term = 4

nth Term = 4*5^n-1

Step-by-step explanation:

The number x - 6 , 2x and x^2 are in G.P

(2x)^2 = (x - 6)x^2

4x^2 = (x - 6)x^2

4 = x - 6

x = 10

10 - 6 = 4

2* 10 = 20

10^ = 100

G.P is 4 , 20 , 100

First Term = 4

Common ratio = 20/4 = 100/20 = 5

nth term = 4* 5^n-1