7. Given a sequence of numbers: $1,3,3,3,5,3,7,3,9,3, \cdots . .$. , the sum of the first 100 terms of this sequence is $\qquad$ _.
Analysis: The key point is the cycle and the pattern of the sequence.
Method 1: The key is to determine the pattern of the sequence. By observation, it is not difficult to find that, except for the first three numbers, the rest are $3,5,3,7 \cdots \cdots$ After removing the first three numbers, we need to find 97 more numbers, $(97-1) \div 2=48$, so there are 48 groups, and the first number in each group is 3, the second number in the 48th group is $5+47 \times 2=99$,
$3,5,3,7,3,9 \cdots \cdots 3$, then the sum of these 97 numbers is
$$
5+7+9+11+\cdots \cdots+99+49 \times 3=2643 \text {, }
$$

Then the sum of the first 100 terms is $2643+1+3+3=2650$
Method 2: By observation, it can be found that the odd terms of the sequence are $1,3,5,7,9 \cdots \cdots$, and the even terms are all $3,3,3,3,3 \cdots \cdots$, so the sum of the sequence is the sum of these two sequences. The sum of the odd terms is the sum of 50 consecutive odd numbers, which is $50^{2}=2500$, and the sum of the even terms is $50 \times 3=150$, so the total sum is $2500+150=2650$