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The three rational numbers between $14 and 15$ are

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1780, 940, 1980

1780, 940, 1980

1780, 940, 1980

1780, 940, 1980

answer is A.

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Detailed Solution

It is given that the two numbers are

14 and 15

.
We know that the rational numbers between x and y are x + d, x + 2d and x + 3d, where

d = y − x n + 1

.
Let

x = 15 and y = 14

.
Here,

x < y

and we must find three rational number, so

n = 3

d = y − x n + 1 = 14 − 15 3 + 1 = 5 − 4 20 4 = 18

The three rational numbers between x and y are

x + d

x + 2 d

and

x + 3 d

∴ x + d = 15 + 180 = 16 + 1 80 = 1780

∴ x + 2 d = 15 + 280 = 16 + 2 80 = 1880 = 940

∴ x + 3 d = 15 + 380 = 16 + 3 80 = 1980

Hence, the three rational numbers between

14 and 15 are 1780, 940, 1980 .

Therefore, the correct option is (1).

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