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Do the numbers in the perimeter row form an arithmetic sequence? If so, what is the common difference, and what is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?

Do the numbers in the perimeter row form an arithmetic sequence If so what is the common difference and what is the recursive formula for the perimeter of a squ class=


Answer :

mhanifa

Answer:

  • Common difference d = 4
  • Recursive formula Pₙ₊₁ = Pₙ+ 4

Step-by-step explanation:

Let the perimeter of the square with length of n be Pₙ.

According to given table we have:

  • P₁ = 4, P₂= 8, P₃ = 12, P₄= 16, P₅= 20

We can put this as a sequence:

  • 4, 8, 12, 16, 20

Common difference is:

  • d = 8 - 4 = 12 - 8 = 16 - 12 = 20 - 16 = 4

The recursive formula for this sequence is:

  • Pₙ₊₁ = Pₙ+ 4

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