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_
Keep practising Sequences, Probability and Counting Theory
Browse all Sequences, Probability and Counting Theory questions for GRE, or explore more Mathematics topics.
Related questions
Pick the bigger countJudge the probability claimsComplete the formulasCount the waysSort each sequence by its patternMatch each sequence idea to its ruleA six-sided number cube is rolled once. What is the probability of rolling a number greateTwo six-sided number cubes are rolled and the faces are summed. What is the probability th