Question

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

Answer 1

Let the required number be $x$ then

$6+x,10+x,14+x,22+x$ are in proportion

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

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

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

$\Rightarrow 132+6x+22x=140+10x+14x$

$\Rightarrow 28x-24x=140+132$

$\Rightarrow 4x=8$

$\Rightarrow x=\frac{8}{4}=2$

$\therefore x=2$