What must be added to the numbers 6,10,14 and 22 so that they are in proportion?

Given :

The given numbers are 6, 10, 14, and 22.

To do :

We have to find the number that should be added to the given numbers so that they are in proportion.

Solution : 
 

Let the number to be added be 'x'.

So, the numbers $6+x, 10+x, 14+x, 22+x$ are in proportion.

Product of extremes $=$ Product of means

$(6+x)(22+x)=(10+x)(14+x)$

$132 + 22x + 6x + x^2 = 140 + 10x + 14x + x^2$

$132+28x = 140+24x$

$28x-24x = 140-132$

$4x = 8$

$x= \frac{8}{4}$

$x=2$

Therefore, the required number is 2.

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Updated on: 10-Oct-2022

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