Which is the correct rule for the sequence (5, 12, 23, 38, ...)?
Answer and explanation
Correct answer: a_n = 2n^2 + n + 2
The governing concept is testing an explicit rule against the sequence, while the first differences help identify its form. The differences are 7, 11, and 15; their second differences are 4 and 4, so a quadratic rule is plausible. Test option A: for n = 1, 2(1)^2 + 1 + 2 = 5; for n = 2, 2(2)^2 + 2 + 2 = 12; for n = 3, 18 + 3 + 2 = 23; and for n = 4, 32 + 4 + 2 = 38. Every listed term is reproduced, so option A is correct. Option B gives 5, 12, 21, 32, while C gives 5, 11, 21, 35; D already gives 5, 11, 17, 23. Thus the distractors fail on later terms.
Frequently asked questions
What is the correct answer to this question?
a_n = 2n^2 + n + 2
Why is this the correct answer?
The governing concept is testing an explicit rule against the sequence, while the first differences help identify its form. The differences are 7, 11, and 15; their second differences are 4 and 4, so a quadratic rule is plausible. Test option A: for n = 1, 2(1)^2 + 1 + 2 = 5; for n = 2, 2(2)^2 + 2 + 2 = 12; for n = 3, 18 + 3 + 2 = 23; and for n = 4, 32 + 4 + 2 = 38. Every listed term is reproduced, so option A is correct. Option B gives 5, 12, 21, 32, while C gives 5, 11, 21, 35; D already gives 5, 11, 17, 23. Thus the distractors fail on later terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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