Discussion
If the sum of an A.P. is the same for p terms and q terms, then the sum of its (p+q) terms is:
Answer: B
Given \(S_p = S_q\). \(\frac{p}{2}[2a+(p-1)d] = \frac{q}{2}[2a+(q-1)d]\). After simplification, we get \(2a(p-q) + d(p^2-p-q^2+q)=0 \Rightarrow (p-q)[2a+d(p+q-1)]=0\). Since p is not equal to q, \(2a+d(p+q-1)=0\). The sum of (p+q) terms is \(S_{p+q} = \frac{p+q}{2}[2a+(p+q-1)d]\). Since the term in the bracket is 0, the sum is 0.
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