Which is the correct general term for the sequence (10,21,34,49,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+8n+1\)
For option D, substituting \(n=1,2,3,4\) gives \(10,21,34,49\), respectively. Hence, the correct general term is \(a_n=n^2+8n+1\). Option A gives the first term as 10, but for \(n=2\) it gives 20, not 21. Exam tip: When first differences are not constant, use the second differences to test a quadratic form \(an^2+bn+c\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+8n+1\)
Why is this the correct answer?
For option D, substituting \(n=1,2,3,4\) gives \(10,21,34,49\), respectively. Hence, the correct general term is \(a_n=n^2+8n+1\). Option A gives the first term as 10, but for \(n=2\) it gives 20, not 21. Exam tip: When first differences are not constant, use the second differences to test a quadratic form \(an^2+bn+c\).
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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