If (a_n=n^2+1), which term is equal to (101)?
Answer and explanation
Correct answer: \(n=10\)
Given \(a_n=n^2+1\), set \(a_n=101\). Then \(n^2+1=101\), so \(n^2=100\) and \(n=10\). Hence, 101 is the 10th term of the sequence. Although the equation also gives \(n=-10\), a term number must be a positive integer, so it is rejected. Exam tip: move the constant term first, then take the square root of the resulting perfect square.
Frequently asked questions
What is the correct answer to this question?
\(n=10\)
Why is this the correct answer?
Given \(a_n=n^2+1\), set \(a_n=101\). Then \(n^2+1=101\), so \(n^2=100\) and \(n=10\). Hence, 101 is the 10th term of the sequence. Although the equation also gives \(n=-10\), a term number must be a positive integer, so it is rejected. Exam tip: move the constant term first, then take the square root of the resulting perfect square.
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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