Which is the (n)th term of the sequence (12,20,30,42,56,\ldots)?
Answer and explanation
Correct answer: \(n^2+5n+6\)
Write the terms as products of consecutive integers: \(12=3\times4\), \(20=4\times5\), \(30=5\times6\), and \(42=6\times7\). Hence, the \(n\)th term is \((n+2)(n+3)\). Expanding gives \(n^2+5n+6\), so option D is correct. Option A gives the first term as 12, but its second term is 19, not 20. Exam tip: For such sequences, factor consecutive terms to identify the pattern in \(n\).
Frequently asked questions
What is the correct answer to this question?
\(n^2+5n+6\)
Why is this the correct answer?
Write the terms as products of consecutive integers: \(12=3\times4\), \(20=4\times5\), \(30=5\times6\), and \(42=6\times7\). Hence, the \(n\)th term is \((n+2)(n+3)\). Expanding gives \(n^2+5n+6\), so option D is correct. Option A gives the first term as 12, but its second term is 19, not 20. Exam tip: For such sequences, factor consecutive terms to identify the pattern in \(n\).
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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