Find the missing term of the series :
1/2, 3/4, 5/8, 7/16, ?. 11/44

Question

Find the missing term of the series :
 1/2, 3/4, 5/8, 7/16, ?. 11/44

Accepted Answer

To find the missing term in the series 1/2, 3/4, 5/8, 7/16, ?, 11/44, we need to identify the pattern in the sequence.

1. **Identifying the Pattern:**
   - The numerators of the fractions are increasing by 2 each time: 1, 3, 5, 7, ?, 11.
   - The denominators of the fractions are powers of 2: 2 (2^1), 4 (2^2), 8 (2^3), 16 (2^4), ?, 44.

2. **Finding the Missing Term:**
   - The next numerator after 7 is 9 (since the pattern is increasing by 2).
   - Observing the denominators, they are powers of 2: 2, 4, 8, 16. The next power of 2 after 16 is 32 (2^5).

Therefore, the missing term should be 9/32.

3. **Explanation of Why Option 2 is Correct:**
   - Option 2 is $\frac{9}{32}$, which matches the pattern identified in the series. The numerator 9 follows the sequence of odd numbers increasing by 2, and the denominator 32 is the next power of 2 after 16.

4. **Explanation of Why Other Options are Incorrect:**
   - Option 1: $\frac{8}{24}$
     - The numerator 8 does not follow the sequence of odd numbers (1, 3, 5, 7, 9, 11).
     - The denominator 24 is not a power of 2.
   - Option 3: $\frac{9}{24}$
     - While the numerator 9 is correct, the denominator 24 is not a power of 2, breaking the pattern.
   - Option 4: $\frac{9}{36}$
     - The numerator 9 is correct, but the denominator 36 is not a power of 2, which does not fit the pattern.

In conclusion, Option 2 ($\frac{9}{32}$) is the correct answer as it fits both the pattern of the numerators and the denominators in the series.