Question 1139208: What is the next number please,
3, -6, 12, 4, 20
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The answer from the other tutor is one POSSIBLE answer that is obtained by logical reasoning.
But there is no single "right" answer to ANY problem like this, because different logical reasoning might produce a different next number.
And, in the end, you could put ANY number you want next and it would be a perfectly valid sequence.
For any problem like this to have any meaning, information must be provided indicating what kind of sequence we are looking for.
---------------------------------------------------------
Note one formal mathematical method that can theoretically be used to solve any problem like this is to assume the numbers are the values of a polynomial evaluated for x=1 to x=5.
5 points can be fit with a polynomial of degree 4; you could use the given values to find the polynomial that produces these numbers and then evaluate the polynomial for x=6 to find an answer that results from formal mathematics.
If you only need to find the next number produced by that polynomial, you can use the method of finite differences to find it, as follows:
3 -6 12 4 20 <-- the given sequence of numbers
-9 18 -8 16 <-- the differences between terms ("first differences")
27 -26 24 <-- second differences
-53 50 <-- third differences
153 <-- fourth difference
To find the next term in the sequence assuming a polynomial of degree 4, repeat the "153" in the row of fourth difference and work back up the array to find the next number in the sequence:
3 -6 12 4 20 263
-9 18 -8 16 243
27 -26 24 227
-53 50 203
153 153
The next number in the sequence -- assuming the sequence is produced by a polynomial of degree 4 -- is 263.
|
|
|
