alleryStart learning →List the first four terms of the geometric sequence with first term 5 and common ratio -2.
A{5, -10, 15, -20}
B{5, 10, 20, 40}
C{5, -10, 20, 40}
D{5, -10, 20, -40}
Answer & Solution
Correct answer: D. {5, -10, 20, -40}
1. Start at 5 and multiply by -2 to get the second term: 5 times -2 = -10.
2. Multiply again: -10 times -2 = 20.
3. Multiply once more: 20 times -2 = -40.
4. The first four terms are {5, -10, 20, -40}, alternating in sign because the ratio is negative.
5. The option {5, -10, 15, -20} alternates signs but grows by 5 each step, so it is an arithmetic pattern rather than repeated multiplication.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_
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