A number theory problem by Ραμών Αδάλια
Number Theory
Level
pending
Determine the next term of the sequence:
32
1
Impossible to tell
8
4
2
0
16
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1 solution
There's infinitely many sequences which begin 2, 4, 8, 16. The fact that the pattern seems to be that a n = 2 n does not mean it actually is. Let me give a simple counter example:
a n = 2 4 1 [ ( π − 3 0 ) n 4 + ( 3 0 8 − 1 0 π ) n 3 + ( 3 5 π − 1 0 7 4 ) n 2 + ( 1 5 6 4 − 5 0 π ) n + 2 4 ( π − 3 0 ) ]
In this sequence, the first 4 terms are 2, 4, 8, and 16, but the next one is π . Do not trust patterns unless you are able to prove them