Find the next term in the series 50,200,100,100,200,50,400,`?"`

Answer

To find the next term in the series 50, 200, 100, 100, 200, 50, 400, let's analyze the pattern step by step.

### Step 1: Identify the series
The given series is: 50, 200, 100, 100, 200, 50, 400, ?

### Step 2: Break down the series into two alternating sequences
1. The first sequence: 50, 100, 200, 400
2. The second sequence: 200, 100, 100, 50

### Step 3: Analyze the first sequence
The first sequence is:
- Start with 50
- 50 multiplied by 2 gives 100
- 100 multiplied by 2 gives 200
- 200 multiplied by 2 gives 400

So, the first sequence is doubling each time.

### Step 4: Analyze the second sequence
The second sequence is:
- Start with 200
- Half of 200 gives 100
- Half of 100 gives 50
- The next term is also 50 (no change)

### Step 5: Predict the next term in the second sequence
Following the pattern in the second sequence, after 50, we will halve it again:
- Half of 50 gives us 25

### Conclusion
Thus, the next term in the series is **25**.