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12471116....1 2 4 7 11 16....

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Q. 12471116....1 2 4 7 11 16....
  1. Identify Pattern: Identify the pattern in the sequence.\newlineThe sequence starts at 11 and the differences between the numbers are increasing by 11 each time: 11, 2−1=12-1=1, 4−2=24-2=2, 7−4=37-4=3, 11−7=411-7=4, 16−11=516-11=5, and so on.
  2. Write Next Numbers: Write down the next few numbers to see the pattern better.\newlineAfter 1616, the next differences are 66, 77, 88, etc. So the next numbers in the sequence would be 16+6=2216+6=22, 22+7=2922+7=29, 29+8=3729+8=37, and so on.
  3. Add Until 100100: Keep adding the next number in the pattern until reaching or exceeding 100100. Continue this process: 37+9=4637+9=46, 46+10=5646+10=56, 56+11=6756+11=67, 67+12=7967+12=79, 79+13=9279+13=92, 92+14=10692+14=106. The sequence has now exceeded 100100.
  4. Count Total Numbers: Count the total numbers in the sequence including the last one that exceeded 100100. The sequence is 1,2,4,7,11,16,22,29,37,46,56,67,79,92,1061, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106. That's 1515 numbers.

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