Question

Choose the correct option that should come next in the series given below:
2, 1, (1/2), (1/4), ...

• A. (1/16)
• B. (2/8)
• C. (1/3)
• D. (1/32)
• E. (1/8)

Hint:

In sequences where terms shrink rapidly and continuously, always test for a common fractional multiplier (Geometric Progression) before trying additive differences.

Answer 1

Answer: (E)

Step 1: Identify the pattern of the sequence.
Term 1 = $2$
Term 2 = $2 \times \frac{1}{2} = 1$
Term 3 = $1 \times \frac{1}{2} = \frac{1}{2}$
Term 4 = $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Step 2: Calculate the next term.
The sequence is a Geometric Progression with a common ratio of $r = 0.5$.
Term 5 = $\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$.