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What kind of sequence is this? 121,144,169,196,…121, 144, 169, 196, \ldots

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Full solution

Q. What kind of sequence is this? 121,144,169,196,…121, 144, 169, 196, \ldots
  1. Identify pattern in sequence: Identify the pattern in the sequence by checking if the numbers are perfect squares. Calculate the square roots of the first few terms:\newline121=11\sqrt{121} = 11, 144=12\sqrt{144} = 12, 169=13\sqrt{169} = 13, 196=14\sqrt{196} = 14.
  2. Recognize square roots pattern: Recognize the pattern in the square roots: 1111, 1212, 1313, 1414. These numbers form an arithmetic sequence with a common difference of 11.
  3. Confirm sequence type: Confirm the sequence type by checking if the square roots continue to increase by 11 for subsequent terms. If the pattern holds, the original sequence is a sequence of consecutive perfect squares.

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