Multiple choice

The term after $\dfrac {1}{20}$ 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 sequence is 1/(1*2), 1/(2*3), 1/(3*4), 1/(4*5). The next term is 1/(5*6) = 1/30.

AI explanation

Looking at the denominators of the sequence 1/2, 1/6, 1/12, 1/20, we see they are formed by multiplying consecutive integers. The next denominator is found by multiplying 5 and 6. Therefore, the next term is 1/30.

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