Multiple choice

Calculate the missing term in the geometric series $\cfrac{1}{4}+x+\cfrac{1}{36}+\cfrac{1}{108}+.....$.

  1. $\cfrac{1}{3}$
  2. $\cfrac{1}{9}$
  3. $\cfrac{1}{12}$
  4. $\cfrac{1}{16}$
  5. $\cfrac{1}{18}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Series: 1/4, x, 1/36, 1/108. Ratio = (1/36) / x = x / (1/4). x^2 = 1/144. x = 1/12.

AI explanation

To find the common ratio of this geometric series, divide the fourth term (1/108) by the third term (1/36), which gives a common ratio r of 1/3. Multiplying the first term (1/4) by this common ratio yields the missing second term: 1/4 * 1/3 = 1/12.