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What kind of sequence is this? 16,25,36,49,16, 25, 36, 49,

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Full solution

Q. What kind of sequence is this? 16,25,36,49,16, 25, 36, 49,
  1. Identify pattern: Step 11: Identify the pattern in the sequence 16,25,36,4916, 25, 36, 49. Calculate the differences between consecutive terms.\newline25−16=925 - 16 = 9,\newline36−25=1136 - 25 = 11,\newline49−36=1349 - 36 = 13.
  2. Check differences pattern: Step 22: Check if the differences form a pattern. Calculate the differences between the differences calculated in Step 11.\newline11−9=211 - 9 = 2,\newline13−11=213 - 11 = 2.
  3. Determine sequence type: Step 33: Determine the type of sequence. Since the second differences are constant (all equal to 22), the sequence is a quadratic sequence.

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