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How many terms are in the finite arithmetic sequence 5, -2, -9, ..., -65?
A10 terms
B12 terms
C9 terms
D11 terms
Answer & Solution
Correct answer: D. 11 terms
1. Find the common difference: -2 - 5 = -7.
2. Write the general term: a_n = 5 + (n - 1)(-7) = 12 - 7n.
3. Set the last term equal to -65: 12 - 7n = -65.
4. Solve: 7n = 77, so n = 11, and the sequence has 11 terms.
5. Option A, 10 terms, comes from solving 5 - 7n = -65, which forgets that the first term uses n = 1, not n = 0.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 ARITHMETIC SEQUENCES_
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