finding the series 100 101 103 107 115 122 127 128 130?

Infinitely many solutions!

+1+2+4+8+7+5+1+2next number would be 134 which is +4

Here is 100 101 103 107 115 122 127 128 130 134 142 149 153.....
1+2+2 = 5 + 122 = 127
1+2+7 = 10
1+0 = 1 + 127 = 128
1+2+8 = 11
1+1 = 2 +128 = 130 and so on.

100,101,103,107,115,122,127,128,130,(?)......

First,
101-100=[1] , 103-101=[2] , 107-103=[4] , 115-107=[8] , 122-115=[7] , 127-122=[5] , 128-127=[[1]] , 130-128=[[2]] ......

Second,
1,2,4,8,7,5,[1,2......]( It is a cycle.)

Finally,
100,101,103,107,115,122,127,128,130,(134)......

If you mean what is next in the series, it would be 134.

I see a bit of a pattern if the last 3 numbers were 127, 130, 131.

The series or the sum of the series?

For the sum use n/2(a+l) where n = 9 in this case because there are 9 terms a=100 the first term in the series and l=130, the last term in the series.