Question

the three numbers are in the ratio 2:5:7. if 7 is subtracted in middle term it forms an AP. find the AP

Answer 1

Answer:

The required AP is 28, 63, 98.

Step-by-step explanation:

It is given that three numbers are in the ratio 2:5:7.

Let the three numbers are 2x, 5x, 7x.

If 7 is subtracted in middle term it forms an AP.

2x, 5x-7, 7x are in AP.

If a,b,c are in AP, then

$2b=a+c$

$2(5x-7)=2x+7x$

$10x-14=9x$

$10x-9x=14$

$x=14$

The value of x is 14.

The AP is

2(14), 5(14)-7, 7(14)

28, 63, 98

Therefore the required AP is 28, 63, 98.

Answer 2

Answer:

The required AP is 28, 63, 98.

Step-by-step explanation:

It is given that three numbers are in the ratio 2:5:7.

Let the three numbers are 2x, 5x, 7x.

If 7 is subtracted in middle term it forms an AP.

2x, 5x-7, 7x are in AP.

If a,b,c are in AP, then

$2b=a+c$

$2(5x-7)=2x+7x$

$10x-14=9x$

$10x-9x=14$

$x=14$

The value of x is 14.

The AP is

2(14), 5(14)-7, 7(14)

28, 63, 98

Therefore the required AP is 28, 63, 98.