Answer: As Devansh Sehta has calculated, there are 82 terms and 82=7×11+5. When each term of S is divided by 7, the remainders, in order are 6, 3, 0, 4, 1, 5, 2, and these repeat.
Explanation:
For any arithmetic sequence, record the remainders when successive terms are divided by n. Then the sum of every set of n consecutive remainders is divisible by 7. In this case, the first 77 terms add to a multiple of 7 as do the 5 remaining terms.