What is the general term of the sequence (2,9,22,41,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2-2n+1\)
The first differences are \(7,13,19\), and the second differences are constant: \(6,6\). Hence, the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=3n^2-2n+1\) gives \(2,9,22,41\), respectively. Option C matches the first two terms but gives \(18\), not \(22\), when \(n=3\). Exam tip: constant second differences usually indicate a rule of the form \(an^2+bn+c\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=3n^2-2n+1\)
Why is this the correct answer?
The first differences are \(7,13,19\), and the second differences are constant: \(6,6\). Hence, the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=3n^2-2n+1\) gives \(2,9,22,41\), respectively. Option C matches the first two terms but gives \(18\), not \(22\), when \(n=3\). Exam tip: constant second differences usually indicate a rule of the form \(an^2+bn+c\).
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.
