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Ronch [10]
4 years ago
5

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

ssion?
Mathematics
1 answer:
OLEGan [10]4 years ago
4 0

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

<em>As their ratios are same so,</em>

\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.

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