What is the (n)th term of the sequence (5,8,13,20,29,\ldots)?
Answer and explanation
Correct answer: \(n^2+4\)
The successive differences are \(3,5,7,9\), which are consecutive odd numbers. The successive differences of \(n^2\) also follow \(3,5,7,\ldots\), so the term has the form \(n^2+c\). Using the first term, \(1^2+c=5\), giving \(c=4\). Hence, the \(n\)th term is \(n^2+4\). The option \(n^2+3\) gives 4 as the first term, so it is incorrect. Exam tip: for a sequence involving squares, check the first and second differences.
Frequently asked questions
What is the correct answer to this question?
\(n^2+4\)
Why is this the correct answer?
The successive differences are \(3,5,7,9\), which are consecutive odd numbers. The successive differences of \(n^2\) also follow \(3,5,7,\ldots\), so the term has the form \(n^2+c\). Using the first term, \(1^2+c=5\), giving \(c=4\). Hence, the \(n\)th term is \(n^2+4\). The option \(n^2+3\) gives 4 as the first term, so it is incorrect. Exam tip: for a sequence involving squares, check the first and second differences.
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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