If \(a_n=\frac{2n^2+1}{n+1}\), what is the value of \(a_4\)?
Answer and explanation
Correct answer: \(\frac{33}{5}\)
For \(a_4\), substitute \(n=4\) into the given formula: \(a_4=\frac{2(4)^2+1}{4+1}=\frac{2\times16+1}{5}=\frac{33}{5}\). Therefore, \(\frac{33}{5}\) is correct. The option \(7\) is incorrect because \(7=\frac{35}{5}\), whereas the correct numerator is \(2\times16+1=33\). Exam tip: after substituting the term number, evaluate the power first, followed by multiplication and addition.
Frequently asked questions
What is the correct answer to this question?
\(\frac{33}{5}\)
Why is this the correct answer?
For \(a_4\), substitute \(n=4\) into the given formula: \(a_4=\frac{2(4)^2+1}{4+1}=\frac{2\times16+1}{5}=\frac{33}{5}\). Therefore, \(\frac{33}{5}\) is correct. The option \(7\) is incorrect because \(7=\frac{35}{5}\), whereas the correct numerator is \(2\times16+1=33\). Exam tip: after substituting the term number, evaluate the power first, followed by multiplication and addition.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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