If (a_n=n^2+2n), for which (n) will (a_n=80)?
Answer and explanation
Correct answer: 8
Given \(n^2+2n=80\), we get \(n^2+2n-80=0\). Factoring gives \((n+10)(n-8)=0\), so \(n=-10\) or \(n=8\). Since a sequence index \(n\) is a positive integer, \(n=8\) is valid. Option 9 is a close distractor, but \(a_9=81+18=99\), not 80. Exam tip: for term-position questions, check whether a negative root is allowed before selecting it.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Given \(n^2+2n=80\), we get \(n^2+2n-80=0\). Factoring gives \((n+10)(n-8)=0\), so \(n=-10\) or \(n=8\). Since a sequence index \(n\) is a positive integer, \(n=8\) is valid. Option 9 is a close distractor, but \(a_9=81+18=99\), not 80. Exam tip: for term-position questions, check whether a negative root is allowed before selecting it.
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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