Which is the nth term of the sequence 5, 12, 21, 32, 45, …?
Answer and explanation
Correct answer: n² + 2n + 2
The governing concept is identifying an explicit rule for a sequence. Test the candidate expressions at n = 1, 2, and 3. The expression n² + 2n + 2 gives 1 + 2 + 2 = 5, 4 + 4 + 2 = 10, so this quick test reveals it does not match the second term; therefore the supplied key and options contain an inconsistency. Checking the sequence carefully, its successive differences are 7, 9, 11, and 13, so the second difference is 2. The actual formula is n² + 4n, which gives 5, 12, 21, 32, and 45. Since that formula is absent from the options, no listed option is correct. This item requires revision rather than a pass.
Frequently asked questions
What is the correct answer to this question?
n² + 2n + 2
Why is this the correct answer?
The governing concept is identifying an explicit rule for a sequence. Test the candidate expressions at n = 1, 2, and 3. The expression n² + 2n + 2 gives 1 + 2 + 2 = 5, 4 + 4 + 2 = 10, so this quick test reveals it does not match the second term; therefore the supplied key and options contain an inconsistency. Checking the sequence carefully, its successive differences are 7, 9, 11, and 13, so the second difference is 2. The actual formula is n² + 4n, which gives 5, 12, 21, 32, and 45. Since that formula is absent from the options, no listed option is correct. This item requires revision rather than a pass.
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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