Question

Choose the correct option that will replace the question mark in the given number series.

100/9, 25/2, 100/7, 50/3, ?

Answer 1

The series given is $\frac{100}{9},\frac{25}{2},\frac{100}{7},\frac{50}{3},?$
Now $\frac{25}{2}$ is in the middle of $\frac{100}{9}\mathrm{and}\frac{100}{7}$
When we multiply numerator and denominator of $\frac{25}{2}$ and add 1 in the denominator we get;
$\frac{25\times 4}{2\times 4+1}=\frac{100}{9}$ which is on the left side of $\frac{25}{2}$.
And when we multiply numerator term of $\frac{25}{2}$ by 4 and denominator term by 3 and adding 1 in the denominator we get;
$\frac{25\times 4}{2\times 3+1}=\frac{100}{7}$ which is on the right side of $\frac{25}{2}$.
Similarly we take now $\frac{50}{3}$ as the middle term of $\frac{100}{7}$ and the question mark.
Similarly as shown in the above process we get; $\frac{50\times 2}{3\times 2+1}=\frac{100}{7}$ which is on the left side of $\frac{50}{3}$.
Then, for the right side of $\frac{50}{3}$ we must continue the above process as $\frac{50\times 2}{3\times 1+1}=\frac{100}{4}$.
Therefore, there will be $\frac{100}{4}$ at the place of question mark.