Multiple choice

Find the next term of the sequence: $\displaystyle\frac{1}{2},\,\frac {1}{6},\,\frac {1}{18},\,\frac {1}{54},\,..........$

  1. $\displaystyle\frac{1}{168}$
  2. $\displaystyle\frac{1}{164}$
  3. $\displaystyle\frac{1}{162}$
  4. $\displaystyle\frac{1}{170}$
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C Correct answer
Explanation

The sequence is a geometric progression with the first term a = 1/2 and common ratio r = 1/3. The next term is (1/54) * (1/3) = 1/162.

AI explanation

The sequence follows a geometric progression where each term is multiplied by 1/3 to get the next term. To find the next number after 1/54, we calculate (1/54) multiplied by 1/3, which is 1/162. The next term is 1/162.

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