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Which of the following sequences has non-constant consecutive first differences but constant second differences?
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Answer and explanation
Correct answer: \(a_n=n^2+1\)
For \(a_n=n^2+1\), the first difference is \(2n+1\), so it changes with \(n\), while the second difference is the constant \(2\). A linear sequence has constant first differences instead. Exam tip: check second differences when an \(n^2\) term appears.
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What is the correct answer to this question?
\(a_n=n^2+1\)
Why is this the correct answer?
For \(a_n=n^2+1\), the first difference is \(2n+1\), so it changes with \(n\), while the second difference is the constant \(2\). A linear sequence has constant first differences instead. Exam tip: check second differences when an \(n^2\) term appears.
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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