If (a_n=4n^2-1), which is the first term greater than (100)?
Answer and explanation
Correct answer: 6th term
We need \(4n^2-1>100\). Thus, \(4n^2>101\), so \(n^2>25.25\). At \(n=5\), \(a_5=99\), which is not greater than 100, whereas \(a_6=143\). Therefore, the first term greater than 100 is the 6th term. Exam tip: after solving an inequality, check the preceding integer term to confirm that the required term is the first one.
Frequently asked questions
What is the correct answer to this question?
6th term
Why is this the correct answer?
We need \(4n^2-1>100\). Thus, \(4n^2>101\), so \(n^2>25.25\). At \(n=5\), \(a_5=99\), which is not greater than 100, whereas \(a_6=143\). Therefore, the first term greater than 100 is the 6th term. Exam tip: after solving an inequality, check the preceding integer term to confirm that the required term is the first one.
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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