what is the next number sequence for 0,10,24,56,112,190
Take a look at the Newton's Method of Divided Differences. The polynomial of lowest degree which fits these data points is
0 + 10(x) + 2(x)(x-1) + (7/3)(x)(x-1)(x-2) + (-1/3)(x)(x-1)(x-2)(x-3)
The next values are 280 364
280
why 280
To identify the next number in a sequence, you need to observe the pattern and find the rule that governs how the numbers are related. Let's analyze the given sequence:
0, 10, 24, 56, 112, 190
At first glance, we can notice that the increasing pattern between the numbers seems irregular. However, if we carefully examine the differences between adjacent terms, a pattern emerges:
10 - 0 = 10
24 - 10 = 14
56 - 24 = 32
112 - 56 = 56
190 - 112 = 78
Looking at these differences, we can observe that they are increasing by an increment of 4, then 6, then 8, then 10. This suggests that the differences between consecutive terms are following a pattern.
To find the next difference, we can increment the difference pattern by 2:
78 + 2 = 80
Now, let's find the next number in the sequence by adding the derived difference to the last number given:
190 + 80 = 270
Therefore, the next number in the sequence is 270.
So, the next number in the given sequence is 270.