If (a_1=2) and (a_{n+1}=2a_n+n^2), what will (a_4) be?
Answer and explanation
Correct answer: 37
Use the recurrence step by step. Thus, a_2=2(2)+1^2=5, a_3=2(5)+2^2=14, and a_4=2(14)+3^2=37. Therefore, 37 is correct. Although 39 is a close distractor, it is not the correct value of 2(14)+3^2. Exam tip: to find a_4, substitute n=1, then n=2, and then n=3; do not substitute n=4 directly.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
Use the recurrence step by step. Thus, a_2=2(2)+1^2=5, a_3=2(5)+2^2=14, and a_4=2(14)+3^2=37. Therefore, 37 is correct. Although 39 is a close distractor, it is not the correct value of 2(14)+3^2. Exam tip: to find a_4, substitute n=1, then n=2, and then n=3; do not substitute n=4 directly.
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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