pawerfict pawerfict
  • 18-08-2018
  • Mathematics
contestada

What is the recursive formula for the sequence 4, 16, 36, 64, 100...?

Respuesta :

DeanR
DeanR DeanR
  • 18-08-2018

Unrecursively, that's

[tex]f(n) = (2n)^2 = 4n^2[/tex]

A quadratic will have a linear first difference:

[tex]f(n+1) - f(n) = 4(n+1)^2 - 4n^2 = 4n^2 + 8n + 4 - 4n^2 = 8n+ 4[/tex]

So we get

f(1) = 4

f(n+1) = f(n) + 8n + 4


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