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

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\frac{40}{35}, \frac{- 48}{42}, \frac{- 56}{49}

\frac{- 40}{35}, \frac{- 48}{42}, \frac{- 56}{49}

\frac{- 40}{35}, \frac{48}{42}, \frac{- 57}{49}

\frac{- 40}{35}, \frac{- 48}{32}, \frac{56}{49}

answer is B.

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Detailed Solution

We are given a pattern of rational numbers as follows,

− 8 7, − 16 14, − 24 21, − 32 28

Now, rewriting the fractions as follows,

− 8 × 1 7 × 1, − 8 × 2 7 × 2, − 8 × 3 7 × 3, − 8 × 4 7 × 4

So, we can see that the base fraction is

− 8 7

, 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

− 8 7

by 5, 6 and 7 and get the rational numbers as follows,

− 8 × 5 7 × 5 = − 40 35 − 8 × 6 7 × 6 = − 48 42 − 8 × 7 7 × 7 = − 56 49

So, the three rational numbers are obtained as

− 40 35

− 48 42

and

− 56 49

.
Hence, the correct option is (2).

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