If (a_1=1) and (a_{n+1}=2a_n+n), what will be (a_5)?
Answer and explanation
Correct answer: 42
Apply the recurrence step by step: \(a_2=2(1)+1=3\), \(a_3=2(3)+2=8\), \(a_4=2(8)+3=19\), and \(a_5=2(19)+4=42\). Therefore, the correct answer is \(42\). A choice such as \(44\) can result from using an incorrect value of \(n\) in the final step. Exam tip: write the value of \(n\) for each step before substituting it in a recurrence relation.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
Apply the recurrence step by step: \(a_2=2(1)+1=3\), \(a_3=2(3)+2=8\), \(a_4=2(8)+3=19\), and \(a_5=2(19)+4=42\). Therefore, the correct answer is \(42\). A choice such as \(44\) can result from using an incorrect value of \(n\) in the final step. Exam tip: write the value of \(n\) for each step before substituting it in a recurrence relation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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