Question

Three integers form an increasing GP.If 3rd nos decreased by 16,we get an AP.If then the 2nd nos decreased by 2,we again get a GP.Find the 3 nos

Answer 1

Answer:

three terms are :

1 , -3 , 9

Explanation:

Suppose three numbers are in GP are $\frac{a}{r} ,   a ,   ar$

3rd numbers is reduced by 16 that is ,  ar - 16

$\frac{a}{r} ,   a ,   (ar-16)$

Airthmatic mean

a = $\frac{\frac{a}{r} + (ar-16) }{2}$  ----------------------(1)

Now 2nd number reduced by 2

$\frac{a}{r} ,   (a - 2) ,   (ar-16)$

Geometric mean

(a-2)² = $\frac{a}{r}*(ar-16)$

a² - 4a + 4 = a² - $\frac{16a}{r}$

-4a + 4 = $\frac{16a}{r}$     ---------------------(2)

Solve equation (1) & (2)

We get a = -3 & r = -3

three terms are :

1 , -3 , 9