ExplanationWhile the sequence is clear (30, 33, 36, 39, 42, etc.), don’t spend time counting to the 80th term. Instead, find a pattern. Each new term in the list adds 3 to the previous term, so determine how many times 3 needs to be added. (By the way, the term “arithmetic sequence” means a sequence in which the same number is added or subtracted for each new term.)

Start with the first term, 30. To get from the first term to the second term, start with 30 and add 3 once. To get from the first term to the third term, start with 30 and add 3 twice. In other words, for the third term, add one fewer instance of 3: twice rather than three times.

To write this mathematically, say: 30 + 3(n-1), where n is the number of the term. (Note: it’s not necessary to write this out, as long as you understand the pattern.)

To get to the 80th term, then, start with 30 and add 3 exactly 79 times:

\(30 + (79 \times 3) = 267\)

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Sandy

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