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A sequence is defined recursively by a_1 = 3 and a_n = 2a_(n-1) - 1 for n >= 2. What is the fifth term?

A31
B17
C33
D35
Answer & Solution
Correct answer: C. 33
1. A recursive rule builds each term from the one before it, starting from a_1 = 3. 2. a_2 = 2(3) - 1 = 5 and a_3 = 2(5) - 1 = 9. 3. a_4 = 2(9) - 1 = 17. 4. a_5 = 2(17) - 1 = 33. 5. Option B, 17, is the fourth term, the classic off-by-one trap when iterating a recursion. _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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