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Tue 28 Nov, 2006 09:41 am
A number sequence:
3, 14, 39, 84, ?
According to the rule by which these numbers are arranged, which number will be next to 84?
A very quick guess would be 196.
Lord Ellpus wrote:A very quick guess would be 196.
Nope...
Come on, find out the true rule beneath them
How about 155?
3 = 1 * 3
14 = 2 * 7 (7 = 3 + 4)
39 = 3 * 13 (13 = 7 + 6)
84 = 4 * 21 (21 = 13 + 8)
155 = 5 * 31 (31 = 21 + 10)
Wow, that's great!
there's another approach of getting it.
3=1*(1+1)+1^3
14=2*(2+1)+2^3
39=3*(3+1)+3^3
84=4*(4+1)+4^3
155=5*(5+1)+5^3
..........
?=n*(n+1)+n^3