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Type the missing number in this sequence:\newline11, _____, 2525, 125125, 625625

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Full solution

Q. Type the missing number in this sequence:\newline11, _____, 2525, 125125, 625625
  1. Identify Pattern: Identify the pattern in the sequence: 11, _\_, 2525, 125125, 625625. We notice that each number seems to be a power of a certain base number.
  2. Determine Base Number: Determine the base number and the pattern of exponents.\newlineThe numbers 11, 2525, 125125, and 625625 are all powers of 55: 505^0, 525^2, 535^3, and 545^4 respectively.
  3. Find Missing Term: Find the missing term in the sequence.\newlineSince the sequence is increasing and we have 505^0 and 525^2, the missing term should be 515^1.\newlineCalculate 515^1 to find the missing number.\newline51=55^1 = 5
  4. Verify Pattern: Verify the pattern with the calculated missing number.\newlineThe sequence now reads: 11 (50)(5^0), 55 (51)(5^1), 2525 (52)(5^2), 125125 (53)(5^3), 625625 (54)(5^4).\newlineThis confirms the pattern of consecutive powers of 55.

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