SOLUTION: Hi I have a problem with formula for series. The 1st 5 numbers are: 5, 10, 17, 26, 37. As you can see differences have differences themselves. I know the sequence would be q

Question 863255: Hi I have a problem with formula for series.
The 1st 5 numbers are: 5, 10, 17, 26, 37.
As you can see differences have differences themselves. I know the sequence would be quadratic because I worked it out: n^2+2n+2
Next part of the question is how many blocks is it needed for 21 patterns.
Formula for series with constant difference is there. But the difference is changing so I don't know what to do, or what to google.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
quadratic series is n^2 + 2n + 2 as you discovered
to find the sum of the first 21 patterns, we need to break this apart
(sum)n^2 + (sum)2n + (sum)2, all from 1 to 21
we know the sum for the power series n^2 is
(n(n+1)(2n+1))/6
the sum for 2n is the sum of even integers
n(x1+xn)/2
the sum of 21 "2"'s is
21*2
now we can put it all together
(21*22*43)/6 + 21*(2+42)/2 + 42 = 3815
you need 3815 blocks

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