Home › GRE General Test › Mathematics › Sequences, Probability and Counting Theory › A sequence is defined recursively by a_1 = 3 and…
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_
Related questions
A 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 thAn electronics store has 10 phones in stock and 4 of them are defective. A customer buys 2How many distinct rearrangements can be made from the letters of the word CARRIER?A sundae bar offers 6 toppings, and any number of them may be chosen, including none. How Twelve sprinters enter a race. In how many different ways can the gold, silver, and bronzeFor a business trip, Priya packs 3 skirts and 5 blouses, and each day decides whether or nAt the beginning of each month, $200 is deposited into a retirement fund that earns 6% ann