googly from ATGS 6

as the number of terms in a row is equal to the number of the row itself , so there are 100 elements in the 100th row.
we have to find the sum of every third element beginning with the second element.
basically that is finding out the coeffs starting from second position in the expansion of (x+a)ⁿ,
so we have to find ¹⁰⁰c₁ +¹⁰⁰c₄ +¹⁰⁰c₇ ......
which can be proven to be 100 + 2⁹⁹ + 2⁵⁰.
please reply.