Discussion
The sum of n terms of a series is \(2n^2 + 3n\). Is the series an A.P.?
Answer: A
The sum of n terms of an A.P. is always a quadratic expression of the form \(An^2+Bn\) with no constant term. Since the given sum \(S_n = 2n^2+3n\) is of this form, the series is an A.P. We can verify this by finding the nth term: \(a_n = S_n - S_{n-1} = (2n^2+3n) - [2(n-1)^2+3(n-1)] = (2n^2+3n) - [2(n^2-2n+1)+3n-3] = 4n+1\). The common difference is \(a_{n} - a_{n-1} = (4n+1) - (4(n-1)+1) = 4\), which is constant.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development