Question

the numbers x-6, 2x, x^2 are in GP. find value of x, 1st term, n th term​

Answer 1

Answer:

x = 10

First Term = 4

nth term = 4 * 5ⁿ⁻¹

Step-by-step explanation:

the numbers x-6, 2x, x^2 are in GP. find value of x, 1st term, n th term​

x -6  , 2x   , x²  are in GP

=> (x - 6)x² = (2x)²

=> (x -6)x² = 4x²

=> (x -6)x² - 4x² = 0

=> x² (x - 6 - 4) = 0

=> x² (x - 10) = 0

=> x = 0  & x = 10

Case 1 : x = 10

4 , 20  , 100

First Term = 4

common ration = 5

nth term = 4 * 5ⁿ⁻¹

Case 2 : x = 0

-6 , 0 , 0

1st Term = 6  & all others terms = 0 as ratio = 0

so this case can be ignored

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