If \(a_n=\frac{n(n-1)}{2}\), what is the value of \(a_5\)?
Answer and explanation
Correct answer: 10
Given \(a_n=\frac{n(n-1)}{2}\), substitute \(n=5\): \(a_5=\frac{5(5-1)}{2}=\frac{5\times4}{2}=10\). Hence, 10 is the correct option. The value 15 would result from using \(\frac{n(n+1)}{2}\), which is not the given rule. Exam tip: to find a particular term from a general rule, first substitute its subscript for \(n\).
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Given \(a_n=\frac{n(n-1)}{2}\), substitute \(n=5\): \(a_5=\frac{5(5-1)}{2}=\frac{5\times4}{2}=10\). Hence, 10 is the correct option. The value 15 would result from using \(\frac{n(n+1)}{2}\), which is not the given rule. Exam tip: to find a particular term from a general rule, first substitute its subscript for \(n\).
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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