Which is the (n)th term of the sequence (8,15,24,35,48,\ldots)?
Answer and explanation
Correct answer: \(n^2+4n+3\)
The consecutive differences are 7, 9, 11, and 13, increasing by 2 each time. Hence, the nth term should be quadratic. For \(a_n=n^2+4n+3\), we get \(a_1=8\), \(a_2=15\), \(a_3=24\), \(a_4=35\), and \(a_5=48\). Therefore, option A is correct. Option B gives \(a_1=8\) but gives \(a_2=16\), so it fails. Exam tip: Test an nth-term option using the first two or three terms.
Frequently asked questions
What is the correct answer to this question?
\(n^2+4n+3\)
Why is this the correct answer?
The consecutive differences are 7, 9, 11, and 13, increasing by 2 each time. Hence, the nth term should be quadratic. For \(a_n=n^2+4n+3\), we get \(a_1=8\), \(a_2=15\), \(a_3=24\), \(a_4=35\), and \(a_5=48\). Therefore, option A is correct. Option B gives \(a_1=8\) but gives \(a_2=16\), so it fails. Exam tip: Test an nth-term option using the first two or three terms.
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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