The sequence (5,8,13,20,29,\ldots) has general term (a_n=n^2+4). Which term is (260)?
Answer and explanation
Correct answer: 16th
Given \(a_n=n^2+4\), set the term equal to 260: \(n^2+4=260\). Thus, \(n^2=256=16^2\), so \(n=16\). Since a term number in a sequence is positive, \(n=-16\) is not considered. The 15th term is \(15^2+4=229\), so it is not correct. Exam tip: quickly recognising perfect squares such as 256 saves time.
Frequently asked questions
What is the correct answer to this question?
16th
Why is this the correct answer?
Given \(a_n=n^2+4\), set the term equal to 260: \(n^2+4=260\). Thus, \(n^2=256=16^2\), so \(n=16\). Since a term number in a sequence is positive, \(n=-16\) is not considered. The 15th term is \(15^2+4=229\), so it is not correct. Exam tip: quickly recognising perfect squares such as 256 saves time.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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