Write the first five terms of the sequence defined by the explicit formula a_n = -3n + 8.
A{8, 5, 2, -1, -4}
B{-3, -6, -9, -12, -15}
C{5, 3, 1, -1, -3}
D{5, 2, -1, -4, -7}
Answer & Solution
Correct answer: D. {5, 2, -1, -4, -7}
1. Substitute n = 1: a_1 = -3(1) + 8 = 5.
2. Substitute n = 2 and n = 3: a_2 = -3(2) + 8 = 2 and a_3 = -3(3) + 8 = -1.
3. Substitute n = 4 and n = 5: a_4 = -3(4) + 8 = -4 and a_5 = -3(5) + 8 = -7.
4. The list is {5, 2, -1, -4, -7}. Starting the count at n = 0 would give 8 first, which is the trap in the option beginning with 8.
_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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