Multiple choice

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

  1. $\dfrac {1}{24}$
  2. $\dfrac {1}{22}$
  3. $\dfrac {1}{30}$
  4. $\dfrac {1}{18}$
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C Correct answer
Explanation

The denominators are 2, 6, 12, 20. These are 1*2, 2*3, 3*4, 4*5. The next denominator is 5*6 = 30.

AI explanation

The denominators of the given fractions are 2, 6, 12, and 20, which are formed by the product of two consecutive natural numbers. The pattern for the denominator is $1 \times 2 = 2$, $2 \times 3 = 6$, $3 \times 4 = 12$, and $4 \times 5 = 20$. Following this product pattern, the next denominator is $5 \times 6 = 30$, giving the next term as 1/30.

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