What is the general term of the sequence (2,11,26,47,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2-1\)
The successive differences are \(9,15,21\), and their second differences are constant: \(6,6\). Hence the rule is quadratic, with coefficient of \(n^2\) equal to \(6/2=3\). Substituting in \(a_n=3n^2-1\) gives \(a_1=2, a_2=11, a_3=26\), and \(a_4=47\). Option D is linear and would require equal first differences. Exam tip: constant second differences usually indicate a quadratic sequence rule.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3n^2-1\)
Why is this the correct answer?
The successive differences are \(9,15,21\), and their second differences are constant: \(6,6\). Hence the rule is quadratic, with coefficient of \(n^2\) equal to \(6/2=3\). Substituting in \(a_n=3n^2-1\) gives \(a_1=2, a_2=11, a_3=26\), and \(a_4=47\). Option D is linear and would require equal first differences. Exam tip: constant second differences usually indicate a quadratic sequence rule.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
