Question : Directions: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
$7 \frac{1}{7}, 8 \frac{2}{6}, 9 \frac{5}{5}, 12 \frac{2}{4}, 16 \frac{2}{3},?$
Option 1: $35 \frac{3}{4}$
Option 2: $16 \frac{4}{4}$
Option 3: $\frac{50}{2}$
Option 4: $15 \frac{2}{4}$
Correct Answer: $\frac{50}{2}$
Solution :
Given:
$7 \frac{1}{7}, 8 \frac{2}{6}, 9 \frac{5}{5}, 12 \frac{2}{4}, 16 \frac{2}{3}, ?$
First, convert all the mixed fractions into fractions –
$ \frac{50}{7}, \frac{50}{6}, \frac{50}{5}, \frac{50}{4}, \frac{50}{3}, ?$
Here, numerators are constant and subtract 1 from the denominator to get the next missing term in the series –
7 – 1 = 6; 6 – 1 = 5; 5 – 1 = 4; 4 – 1 = 3; 3 – 1 = 2
So, the series is: $7 \frac{1}{7}, 8 \frac{2}{6}, 9 \frac{5}{5}, 12 \frac{2}{4}, 16 \frac{2}{3}, \frac{50}{2}$.
So, $\frac{50}{2}$ is the missing term in the series. Hence, the third option is correct.
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