what are the next 3 numbers after -1,+4,-9,+16
looks like we are taking the perfect squares and alternating them - and +
A perfect square is any rational number that is the square of another rational number.
1 ^ 2 = 1
2 ^ 2 = 4
5 ^ 2 = 25
6 ^ 2 = 36
7 ^ 2 = 49
etc.
Your series is a perfect square with negative odd numbers.
The next 3 numbers are :
- 25 , 36 , - 49
To find the next three numbers in the pattern -1, +4, -9, +16, we need to identify the underlying rule or pattern.
Looking at the given sequence, we can observe that the first difference between consecutive terms alternates between increasing and decreasing. The pattern for the first differences is as follows:
+5, -13, +25
Although the first differences do not follow a simple arithmetic progression, we can take a closer look at the second differences to find if they exhibit any regularity. The second differences of the given sequence are:
-18, +38
By examining the second differences, we can see that they are not constant. This indicates that the sequence does not follow a quadratic pattern (second-degree polynomial).
However, we can observe that the second differences are increasing by 20 each time. This suggests that the sequence may follow a cubic pattern (third-degree polynomial).
To find the next three terms, we can calculate the next second difference and continue the cubic pattern by adding the next three terms.
Given that the second difference is increasing by 20, we can calculate the next second difference by adding 20 to the last observed second difference:
+38 + 20 = +58
Now we can continue the cubic pattern by adding the next three terms:
-1 (the last given term)
+16 (first difference +38)
+58 (next second difference)
+122 (second difference +58)
+224 (second difference +102)
Therefore, the next three numbers in the sequence -1, +4, -9, +16 are: +16, +58, +122, +224.