1, 100, 1001, 10000, 11001, 100100, ?

The given sequence is: 1, 100, 1001, 10000, 11001, 100100, ?

Let us break down the sequence step by step and look for the pattern:

• 1: The first term is a single digit.
• 100: The second term is the next power of 10, which is 10^2.
• 1001: The third term is a number that consists of 1, followed by three zeros, and then another 1.
• 10000: The fourth term is 10,000, which is 10^4, a power of 10.
• 11001: The fifth term starts to deviate, with the number 11001 following a specific pattern where the digits are incrementing in a somewhat structured way. If you carefully observe, this is 10000 + 1001.
• 100100: The sixth term follows a similar rule as the previous one, showing a continuation of the trend.

Now, based on the numbers given, we can deduce that the next number in the sequence continues from the previous pattern. Following the trends of adding values incrementally, the next number in the sequence is:

110001.

As we analyze this further, we can see that 11001 plays a significant role in the formation of these numbers. Every term incorporates a combination of powers of 10 and the number 11001 either directly or through its influence in the structure.

Thus, the sequence becomes clearer as:

• 1
• 100
• 1001
• 10000
• 11001
• 100100
• 110001

Therefore, the next number in the sequence is 110001, as each number builds upon the previous one by adding increments related to the number 11001.

Answer : 110001