Find the next three rational numbers in the pattern −8 7 , −16 14 , −24 21 , −32 28 .

# Find the next three rational numbers in the pattern .

1. A
$\frac{40}{35},\frac{-48}{42},\frac{-56}{49}$
2. B
$\frac{-40}{35},\frac{-48}{42},\frac{-56}{49}$
3. C
$\frac{-40}{35},\frac{48}{42},\frac{-57}{49}$
4. D
$\frac{-40}{35},\frac{-48}{32},\frac{56}{49}$

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### Solution:

We are given a pattern of rational numbers as follows,

Now, rewriting the fractions as follows,

So, we can see that the base fraction is , and its numerator and denominator are multiplied by 1, 2, 3 and 4 to generate new rational numbers.
So, in order to write 3 more ration numbers in the series, we will repeat this process by multiplying the numerator and denominator of by 5, 6 and 7 and get the rational numbers as follows,

So, the three rational numbers are obtained as  , and .
Hence, the correct option is (2).

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