Elementary English & Math Education Tips

5th grade math problem: if set 1 has 3 dots, set 2 has 6, and set 3 has 10, how many does set n=100 have?

my spouse came up with 5151 by counting *every* single set, but there HAS to be a formula.

S1 = 3
S2 = 3 + 3
S3 = 3 + 3 + 4
S4 = 3 + 3 + 4 + 5
…
Sn = 3 + 3 + 4 + 5 + … + (n+1)
Sn = 3 + (3+n+1)*(n-1)/2
Sn = (6 + (n+4)*(n-1))/2
Sn = (n^2 + 3n + 2)/2

S100 = (100^2 + 3*100 + 2)/2
= (10000 + 302)/2
= 10302/2
= 5151

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