Which is the correct general term for the sequence (5,12,23,38,57,\ldots)?
Answer and explanation
Correct answer: (a_n=2n^2+n+2)
To identify a general term, substitute small positive values of \(n\) into each proposed formula and compare them with the listed sequence. For the proposed expression \(a_n=2n^2+n+2\), at \(n=1\) we get \(2+1+2=5\); at \(n=2\), we get \(8+2+2=12\); and at \(n=3\), we get \(18+3+2=23\). These match the first three terms.
The formula also gives \(a_4=2(4^2)+4+2=32+4+2=38\) and \(a_5=2(5^2)+5+2=50+5+2=57\), matching the next terms as well. Hence option D is correct. Checking several terms is important because matching only one term could happen by chance. The other formulas fail when tested against the sequence.
Frequently asked questions
What is the correct answer to this question?
(a_n=2n^2+n+2)
Why is this the correct answer?
To identify a general term, substitute small positive values of \(n\) into each proposed formula and compare them with the listed sequence. For the proposed expression \(a_n=2n^2+n+2\), at \(n=1\) we get \(2+1+2=5\); at \(n=2\), we get \(8+2+2=12\); and at \(n=3\), we get \(18+3+2=23\). These match the first three terms.
The formula also gives \(a_4=2(4^2)+4+2=32+4+2=38\) and \(a_5=2(5^2)+5+2=50+5+2=57\), matching the next terms as well. Hence option D is correct. Checking several terms is important because matching only one term could happen by chance. The other formulas fail when tested against the sequence.
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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