Next number in the number sequence is 22, 11, 33, 16.5, 49.5, ?

Concept

In an alternating-operation series, two different rules act in strict rotation: one rule transforms a term into the next, then a second rule transforms that result into the term after it, and the two rules keep alternating along the whole chain. To extend such a series you first identify the pair of operations, then apply whichever operation is due at the missing position.

Application

Compare each consecutive pair of terms to expose the two alternating rules:

1. 22 to 11: the term is multiplied by 0.5 (halved).

2. 11 to 33: the term is multiplied by 3 (tripled).

3. 33 to 16.5: multiplied by 0.5 again.

4. 16.5 to 49.5: multiplied by 3 again.

So the rule alternates ×0.5, ×3, ×0.5, ×3, …. The step from 49.5 to the missing term is therefore the ×0.5 (halving) step:

49.5 × 0.5 = 24.75

Cross-check

Run the multipliers the other way to confirm the rhythm: 24.75 × 3 = 74.25 would be the next term, continuing the ×3 step — consistent with the established ×0.5, ×3 alternation. The halving applied to 49.5 gives 24.75.