SOLUTION: what is the next three terms of 4,1,0,1,4,9

Question 1164001: what is the next three terms of 4,1,0,1,4,9

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

The next three terms can be 16, 25, 36,

but also can be any other three numbers.

The question, as it is posed, makes no mathematical sense.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

ANY problem like this -- where a sequence of numbers is given, you are asked to find the next number(s) in the sequence, and no further information is given -- is invalid.

In this particular example, it APPEARS that the numbers are consecutive perfect squares:
(-2)^2=4
(-1)^2=1
0^2=0
1^2=1
2^2=4
3^2=9

So it might LOOK AS IF the next three numbers should be
4^2=16
5^2=25
6^2=36

But there is NOTHING in the statement of the problem that tells us that is the pattern; in fact, ANY next three numbers will make a valid sequence.

So you can GUESS that the next three numbers in this example will be 16, 25, and 36.... But there is no way of knowing if that answer is "right".

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