What is the general term of the sequence (−1, 0, 3, 8, …)?
Answer and explanation
Correct answer: aₙ = n² − 2n
To identify the explicit rule, substitute the position n into each candidate and compare the resulting values. For option A, aₙ = n² − 2n: at n = 1 it gives 1 − 2 = −1; at n = 2 it gives 4 − 4 = 0; at n = 3 it gives 9 − 6 = 3; and at n = 4 it gives 16 − 8 = 8. Therefore option A exactly reproduces the sequence. Option B gives 0 as the first term, option C gives −1, 1, 3, 5, and option D gives 2, 6, 12, 20. The governing idea is that an explicit rule must produce the correct term directly for every allowed position, not merely match one or two values.
Frequently asked questions
What is the correct answer to this question?
aₙ = n² − 2n
Why is this the correct answer?
To identify the explicit rule, substitute the position n into each candidate and compare the resulting values. For option A, aₙ = n² − 2n: at n = 1 it gives 1 − 2 = −1; at n = 2 it gives 4 − 4 = 0; at n = 3 it gives 9 − 6 = 3; and at n = 4 it gives 16 − 8 = 8. Therefore option A exactly reproduces the sequence. Option B gives 0 as the first term, option C gives −1, 1, 3, 5, and option D gives 2, 6, 12, 20. The governing idea is that an explicit rule must produce the correct term directly for every allowed position, not merely match one or two values.
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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