Question

What number should be added to each of the three numbers 1, 7 and 19 so that the resulting three numbers form a geometric progression?

Answer 1

Answer:

The geometric progression is 6,12,24.

Step-by-step explanation:

Given : Three numbers 1, 7 and 19.

To find : What number should be added to each of  numbers so that the resulting three numbers form a geometric progression?

Solution :

We know that, In geometric progression the ratio between two number is same.

Let x be the number added in three numbers.

So, The sequence form is 1+x, 7+x, 19+x

As their ratios are same so,

$\frac{7+x}{1+x}=\frac{19+x}{7+x}$

Solve the expression,

$(7+x)(7+x)=(19+x)(1+x)$

$49+7x+7x+x^2=19+19x+x+x^2$

$49+14x=19+20x$

$6x=30$

$x=5$

Terms are

$1+x=5+1=6$

$7+x=7+5=12$

$19+x=19+5=24$

Therefore, The geometric progression is 6,12,24.