Find the rule behind this number sequence, and list the next three numbers:
..., 2, 23/3, 15, 121/5, 106/3, ..., ..., ...
(Hint: the first number listed is the second term of the sequence)
(In reply to
Puzzle Answer by K Sengupta)
Multiplying the terms of the given sequence by 2,3,4,5,6... in turn, we obtain:
4,23,60,121,212
Now, we observe that:
4 = 2^3 - 4 121 = 5^3 -4
23= 3^3 - 4 212 = 6^3 - 4
60 = 4^3 - 4
Accordingly, the given sequence is defined as:
T(n) = (n^3 -4)/n
Substituting n=7,8, 9 in turn, we obtain:
T(7) = 339/7
T(8) = 508/8 = 127/2
T(9) = 725/9
Also, T(1) =-3/1=-3
Consequently,
-> The given sequence is defined as:
T(n) = (n^3-4)/n
-> The next three terms of the sequence is given by:
339/7, 127/2 and 729/2
-> The first term of the sequence is -3
Explanation to the Puzzle Answer
