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How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number \(-512\) appears?

 May 30, 2022
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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

 May 30, 2022

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