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

Concept: A number series formed by repeated division (a geometric progression) is generated by multiplying each term by a fixed common ratio to get the next term. To extend such a series, first find the common ratio from the given terms, then apply it once more to the last term.

1. The first two terms are 2 and 1. Dividing 1 by 2 gives a ratio of 1/2, so each term is half of the one before it.

2. Check this ratio against the next pair: 1 and 1/2. Half of 1 is 1/2, which matches the third term.

3. Check again with 1/2 and 1/4. Half of 1/2 is 1/4, which matches the fourth term — the ratio 1/2 is confirmed.

4. Apply the same ratio to the last given term, 1/4: half of 1/4 is 1/8.

This can be verified using the general term of a geometric progression, an = a1 × rn−1, with first term a1 = 2 and common ratio r = 1/2. The fifth term is 2 × (1/2)4 = 2/16 = 1/8, matching the step-by-step result above.

So the number that comes next in the series is 1/8.