Question

The next term in the sequence $\frac{1}{2},\frac{1}{6},\frac{1}{12},\frac{1}{20},....$ is

• A. $\frac{1}{24}$
• B. $\frac{1}{22}$
• C. $\frac{1}{30}$
• D. $\frac{1}{18}$

Answer 1

The correct option is C $\frac{1}{30}$

The given sequence is:

$\frac{1}{2},\frac{1}{6},\frac{1}{12},\frac{1}{20},....$

In the above sequence, let us only consider the denominators of each term as follows:

The denominators of the second and first term has a difference of $4$ that is $6-2=4$,

The denominators of the third and second term has a difference of $6$ that is $12-6=6$,

The denominators of the fourth and third term has a difference of $8$ that is $20-12=8$,

Similarly, the denominators of the fifth and fourth term will have a difference of $10$ that is $30-20=10$,

Hence, the $5$th term of the given sequence is $\frac{1}{30}$.