Number Series: 50, 200, 100, 100, 200, 50, 400, ?

To identify the pattern in the given number series, let's analyze the sequence step by step:

Step 1: Identifying Patterns
- The series begins with 50 and ends with an unknown value.
- The numbers in the series are 50, 200, 100, 100, 200, 50, 400.

Step 2: Analyzing the Sequence
- If we observe carefully, we can see that the series consists of two repeating patterns.
- The first pattern is: 50, 200, 100, 100.
- The second pattern is: 200, 50, 400.

Step 3: Identifying the First Pattern
- The first pattern appears to be a decreasing sequence followed by two identical numbers.
- The numbers in the first pattern are: 50, 200, 100, 100.
- The decreasing part of the pattern is obtained by multiplying each number by 4/2 = 2.
- So, the next number in the first pattern would be 100 * 2 = 200.

Step 4: Identifying the Second Pattern
- The second pattern seems to be an increasing sequence followed by a number that is double the previous number.
- The numbers in the second pattern are: 200, 50, 400.
- The increasing part of the pattern is obtained by dividing each number by 4/2 = 2.
- So, the next number in the second pattern would be 400 * 2 = 800.

Step 5: Determining the Next Number
- Now that we have identified the two patterns, we need to determine which pattern should be followed next in the series.
- Since the previous number in the series was 400, we should continue with the second pattern.
- Therefore, the next number in the series would be 400 * 2 = 800.

Conclusion
- Based on the analysis, the next number in the series after 400 is 800.
- Hence, the complete number series is: 50, 200, 100, 100, 200, 50, 400, 800.

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