There are 22 terms in the sum, since there is a difference of 5 between consecutive terms, and 5n + 1 = 1 for n = 0 and 5n + 1 = 106 for n = 21.
Now, if
S = 1 + 6 + 11 + … + 96 + 101 + 106
then it's also true that
S = 106 + 101 + 96 + … + 11 + 6 + 1
Notice that terms in the same position of these two copies of S add up to 107 :
1 + 106 = 107
6 + 101 = 107
11 + 96 = 107
and so on.
If we then combine S with its reverse, we get
2S = 107 + 107 + … + 107 + 107
but the right side consists of 22 terms, so
2S = 107 • 22
S = 107 • 22 / 2
S = 1177