7.

The third $=$ in the hundredth line



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【Answer】4851
【Analysis】Key points: Number sequence rules, Permutations and combinations (Pascal's Triangle)
(Method 1) Observe the third number in each row, and find that the first and second rows do not have it. Starting from the third row, the third number in each row is $1, 3, 6, 10, 15, 21, \ldots$. The pattern is: from the 3rd row to the 4th row, it is +2; from the 4th row to the 5th row, it is +3; from the 5th row to the 6th row, it is +4, ..., from the 99th row to the 100th row, it is +98. The third number in the 100th row is: $3+3+4+5+\cdots+98=1+2+3+4+5+\cdots+98=4851$ (Method 2) This triangle is Pascal's Triangle, where all the numbers are combinations. The $m$-th number in the $n$-th row is $C_{n-1}^{m-1}$. The third number in the 100th row is $C_{100-1}^{3-1}=C_{99}^{2}=99 \times 98 \div 2=4851$