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A sequence is defined by the explicit formula a_n = -3n + 8. Which term of the sequence equals -22?
AThe 9th term
BThe 10th term
CThe 8th term
DThe 11th term
Answer & Solution
Correct answer: B. The 10th term
1. An explicit formula gives any term directly from its position n, so set the formula equal to -22.
2. Solve -3n + 8 = -22: subtract 8 from both sides to get -3n = -30.
3. Divide by -3 to get n = 10, so the 10th term equals -22.
4. Checking n = 9 gives -19 and n = 11 gives -25, so neither neighboring position works.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 SEQUENCES AND THEIR NOTATIONS_
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