If \(a_n=\frac{n(n+1)}{2}\), at which term will \(a_n=45\)?
Answer and explanation
Correct answer: 9th term
Given \(\frac{n(n+1)}{2}=45\), we get \(n(n+1)=90\), so \(n^2+n-90=0\). Factoring gives \((n-9)(n+10)=0\). Since a term number must be positive, \(n=9\). Therefore, 45 is the 9th term of the sequence. The 10th term is \(\frac{10\times11}{2}=55\), so it is not correct. Exam tip: Clear the denominator first and take the positive root of the resulting quadratic equation.
Frequently asked questions
What is the correct answer to this question?
9th term
Why is this the correct answer?
Given \(\frac{n(n+1)}{2}=45\), we get \(n(n+1)=90\), so \(n^2+n-90=0\). Factoring gives \((n-9)(n+10)=0\). Since a term number must be positive, \(n=9\). Therefore, 45 is the 9th term of the sequence. The 10th term is \(\frac{10\times11}{2}=55\), so it is not correct. Exam tip: Clear the denominator first and take the positive root of the resulting quadratic equation.
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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