Question

The missing term in the series 2,1, \(\frac{1}{2}\),\(\frac{1}{4}\), is

• A. \(\frac{1}{3}\)
• B. \(\frac{1}{8}\)
• C. \(\frac{2}{8}\)
• D. \(\frac{1}{16}\)

Answer 1

The Correct Option is B

To find the missing term in the series \(2, 1, \frac{1}{2}, \frac{1}{4}\), we need to identify the pattern in the given sequence. 

1. The first term is \(2\).
2. The second term is \(1\), which is \(\frac{1}{2}\) of the first term \(2\). This suggests that each term might be half of the previous term.
3. The third term is \(\frac{1}{2}\), which is \(\frac{1}{2}\) of the second term \(1\).
4. The fourth term is \(\frac{1}{4}\), which is \(\frac{1}{2}\) of the third term \(\frac{1}{2}\).

From this pattern, we can see that each term is obtained by multiplying the previous term by \(\frac{1}{2}\).

So, the missing term before \(\frac{1}{2}\) in the series is:

• Term before \(\frac{1}{2}\): Multiply \(\frac{1}{2}\) by \(\frac{1}{2}\) which is \(\frac{1}{4}\). However, \(\frac{1}{4}\) is already given in the series after the missing term. Thus, we calculate the term between \(1\) and \(\frac{1}{4}\)
• The term \(x\) between \(1\) and \(\frac{1}{4}\) is obtained as \(x = \frac{1}{4} \text{ divided by } \left( \text{multiplied by } \frac{1}{2}\right)\).
• Calculating gives: \[ x = 1 \times \frac{1}{2} = \frac{1}{2} \]
• Therefore, since multiplying term \(x\) by \(\frac{1}{2}\): \[ x \times \frac{1}{2} = \frac{1}{8} \]

 

Hence, the missing term in the series is \(\frac{1}{8}\).

The correct option is: \(\frac{1}{8}\)