Question

If 4/9 x 4/27 are in gp series then find value of x

Answer 1

Step-by-step explanation:

We know that if a,b,c are in gp.

then b²=ac

since common ratio is same

Answer 2

x = 4 / 9$\sqrt{3}$ or x = - 4 / 9$\sqrt{3}$

Given:

Geometric Progression =  4/9, x, 4/27

To Find:

The value of x.

Calculating:

In a GP the ratio of the second term to the first term and the third term to the second term will always be equal.

This ratio is known as the common ratio of a GP.

Applying this logic in this GP we find out the value of x.

a2 / a1 = a3 / a2

Substituting the values known to us in this equation we get:

x / 4 / 9 = 4 / 27 / x

9x / 4 = 4 / 27x

Cross multiplying we get:

(27x) (9x) = (4) (4)

243 x^2 = 16

x^2 = 16 / 243

x = $\sqrt{\frac{16}{243}}$

= 4 / 9$\sqrt{3}$

Therefore, x can have two values which can be as follows:

x = 4 / 9$\sqrt{3}$ or x = - 4 / 9$\sqrt{3}$