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Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$ and have at least $3$ elements?

1. $3$
2. $4$
3. $6$
4. $7$
5. $8$

1