Question

Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?

• A. 1/3
• B. 1/8
• C. 2/8
• D. 1/16

Hint:

In any decreasing geometric progression where terms are halved successively, the denominators of the fractions double: $2, 4, 8, 16 \dots$ This makes finding the next term very easy.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To find the next number in a sequence, we must identify the mathematical pattern or rule governing the transition from one term to the next.
Key Formula or Approach:
Let us check the ratio between consecutive terms ($r = \frac{a_{n+1}}{a_n}$):
- Ratio between 1st and 2nd term: $\frac{1}{2}$
- Ratio between 2nd and 3rd term: $\frac{1/2}{1} = \frac{1}{2}$
- Ratio between 3rd and 4th term: $\frac{1/4}{1/2} = \frac{1}{2}$
Since the common ratio is constant, this is a geometric progression with $r = \frac{1}{2}$.

Step 2: Detailed Explanation:
The pattern is that each term is exactly half of the preceding term:
- $2 \times \frac{1}{2} = 1$
- $1 \times \frac{1}{2} = \frac{1}{2}$
- $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$
Following this rule, the next term in the series is:
- $\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$

Step 3: Final Answer:
The next number is 1/8, which corresponds to Option (B).