Look at this series: 36, 34, 30, 28, 24, . . . What number should come next ?

Concept: In an alternating two-step subtraction series, the terms are not reduced by one fixed difference; instead, two different constant amounts are subtracted in a fixed repeating order (first one amount, then the other, then back to the first, and so on). To find the next term, first identify the two repeating amounts and their order, then continue the same cycle for one more step.

Application:

1. 36 − 2 = 34

2. 34 − 4 = 30

3. 30 − 2 = 28

4. 28 − 4 = 24

5. 24 − 2 = 22 (the cycle returns to subtracting 2, since the previous step subtracted 4)

Cross-check: Split the series into two interleaved subsequences by position — the 1st, 3rd, 5th terms (36, 30, 24) and the 2nd, 4th terms (34, 28). Each subsequence falls by a constant 6 (36 → 30 → 24 and 34 → 28 → 22), confirming the next term independently.

So the next number in the series is 22.