Question

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?

Answer 1

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

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