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Who Ordered the Pi? (Posted on 2003-04-21) Difficulty: 4 of 5
What is the next number in this sequence?

1, 4, 9, 16, 25, pi

The sequence is not arbitrary. Create a mathematical function that generates this sequence.

See The Solution Submitted by Bryan    
Rating: 1.7778 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
The 5th degree vs. The interrupted sequence | Comment 1 of 11
Two ideas came to me soon after seeing this problem.

Idea 1
The sequence can be interpreted as a series of points: (1,1),(2,4),(3,9),(4,16),(5,25),(6,pi)

Construct a polynomial passing through those points: f(x) = (x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(pi-36)/120+x^2

f(7) = 6*pi-167

Idea 2
The sequence is the perfect squares with pi substituted for 36. The next term is then 49.
  Posted by Brian Smith on 2003-04-21 05:52:35
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