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.
Two ideas came to me soon after seeing this problem.
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
The sequence is the perfect squares with pi substituted for 36. The next term is then 49.