Find the missing term in the following series: 1, 2, 6, 7, 21, 22, 66, 67, ?

In an alternating-operation number series, consecutive terms are generated by cycling between two distinct operations (such as addition and multiplication) rather than a single fixed rule; the missing term is found by first identifying both operations from the consecutive term pairs already given, then applying whichever operation is next in that established cycle.

1. 1 + 1 = 2

2. 2 x 3 = 6

3. 6 + 1 = 7

4. 7 x 3 = 21

5. 21 + 1 = 22

6. 22 x 3 = 66

7. 66 + 1 = 67

8. 67 x 3 = 201

Every addition step above adds exactly 1, and every multiplication step multiplies by exactly 3, consistently across all six known transitions. Since the last operation applied (66 to 67) was addition, the next operation in the alternating cycle must be multiplication, giving 67 x 3 = 201. Hence, the missing term is 201.