What is the (n)th term of the sequence (3,9,18,30,45,\ldots)?
Answer and explanation
Correct answer: \(\frac{3n(n+1)}{2}\)
The successive differences are \(6,9,12,15,\ldots\), so the second differences are constant at \(3\). The terms are three times the triangular numbers: \(3\times1, 3\times3, 3\times6, 3\times10,\ldots\). Since the \(n\)th triangular number is \(\frac{n(n+1)}{2}\), the required term is \(\frac{3n(n+1)}{2}\). For example, \(3n^2\) gives 12 when \(n=2\), whereas the second term is 9. Exam tip: a constant second difference indicates a quadratic sequence.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3n(n+1)}{2}\)
Why is this the correct answer?
The successive differences are \(6,9,12,15,\ldots\), so the second differences are constant at \(3\). The terms are three times the triangular numbers: \(3\times1, 3\times3, 3\times6, 3\times10,\ldots\). Since the \(n\)th triangular number is \(\frac{n(n+1)}{2}\), the required term is \(\frac{3n(n+1)}{2}\). For example, \(3n^2\) gives 12 when \(n=2\), whereas the second term is 9. Exam tip: a constant second difference indicates a quadratic sequence.
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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