What is the general term of the sequence \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
Answer and explanation
Correct answer: \(a_n=\frac{n}{2}\)
This is an arithmetic progression with first term \(\frac{1}{2}\) and common difference \(\frac{1}{2}\). Therefore, \(a_n=\frac{1}{2}+(n-1)\frac{1}{2}=\frac{n}{2}\). Check: for \(n=1\), \(a_1=\frac{1}{2}\), and for \(n=2\), \(a_2=1\). The rule \(a_n=n\) gives the first term as 1, so it is incorrect. Exam tip: substitute the first two or three values of \(n\) to verify a general term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=\frac{n}{2}\)
Why is this the correct answer?
This is an arithmetic progression with first term \(\frac{1}{2}\) and common difference \(\frac{1}{2}\). Therefore, \(a_n=\frac{1}{2}+(n-1)\frac{1}{2}=\frac{n}{2}\). Check: for \(n=1\), \(a_1=\frac{1}{2}\), and for \(n=2\), \(a_2=1\). The rule \(a_n=n\) gives the first term as 1, so it is incorrect. Exam tip: substitute the first two or three values of \(n\) to verify a general term.
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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