If (a_1=1) and (a_{n+1}=2a_n+1), what is (a_4)?
Answer and explanation
Correct answer: 15
The recursive rule says that each new term is twice the previous term plus 1. Thus, a_2=2(1)+1=3, a_3=2(3)+1=7, and a_4=2(7)+1=15. Therefore, the correct answer is 15. The value 7 is a close distractor because it is a_3, not a_4. Exam tip: start with the given first term and apply the rule one step at a time.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The recursive rule says that each new term is twice the previous term plus 1. Thus, a_2=2(1)+1=3, a_3=2(3)+1=7, and a_4=2(7)+1=15. Therefore, the correct answer is 15. The value 7 is a close distractor because it is a_3, not a_4. Exam tip: start with the given first term and apply the rule one step at a time.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.
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