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.
(In reply to
The 5th degree vs. The interrupted sequence by Brian Smith)
True. Part I of your methodology gives the precise formula for the given sequence.
Also, in my opinion, your solution is correct, since the official solution is inclusive of some inadvertent typographical anomalies.
The appropriate methodology in support of this assertion is furnished hereunder as follows:
Let S(p) denote the pth term of the given sequence.
Then, we observe that:
S(1) = 1 = 1^2
S(2) = 4 = 2^2
S(3) = 9 = 3^2
S(4) = 16 = 4^2
S(5) = 25 = 5^2
S(6) = pi = 6^2 + (pi-36)
This leads us to assert that S(p) = p^2 + (pi-36)*G(p) ....(*)
In (*), we observe that G(p) = 0, whenever p = 1,2,3,4,5 and:
G(p) = 1, if G(p) = 6
This is satisfied for G(p) = (p-1)(p-2)(p-3)(p-4)(p-5)/5!
Now, G(7) = 6!/5! = 6, so that:
S(7) = 7^2 + (pi-36)*6
= 49 + 6*pi - 216
= 6*pi - 167
Thus, it is now apparent, that in the final steps of the official solution, for n=7,it should have been "49 + (pi-36)6!/5!" rather than "36 + (pi-36)6!/5!" leading to "6*pi - 167" instead of "6*pi - 180".
Edited on April 2, 2008, 6:02 am
re: The 5th degree vs. The interrupted sequence
