Question

If x-2,x+ 1, and x+7 are 1st 3terms in GP then find the value of x and find 11th term of it​

Answer 1

Answer:

3072

Step-by-step explanation:

Since, x-2, x+1, and x+7 are in GP:

$\frac{x + 1}{x - 2} = \frac{x + 7}{ x+ 1}$

Therefore,

${x}^{2} + 2x + 1 = {x}^{2} + 5x - 14$

Therefore,

$3x = 15$

Therefore,

$x= 5$

Therefore, first term is 3, second term is 6 and third term is 12.

Therefore, the common divisor (r) is 6/3 = 2

Therefore by A n formula eleventh term is

$a {r}^{n - 1}$

Therefore eleventh term is,

$3 \times {2}^{10}$

$3 \times 1024$

$3072$

Therefore, eleventh term of the given GP is 3072.