How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number \(-512\) appears?
85 - 88 == - 3 - this is the common difference
- 512 ==88 + (- 3 *( N - 1))
- 512 ==88 + - 3N + 3
- 512 - 88 - 3 ==- 3N
- 603 == - 3N
N ==- 603 / -3
N ==201 - this term number gives - 512
So: 201 - 1 ==200 terms before you get to - 512