wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the sum of the first p terms of an AP is the same as the sum of its first q terms ( where pq ) then show that the sum of its first (p+q) terms is zero.

Open in App
Solution

Let a be the first term and d be the common difference of the given AP. Then,
Sp=Sq
p2[2a+(p1)d]=q2[2a+(q1)d]

(pq)(2a)=(qp)(q+p1)d
2a=(1pq)d ......(1)
Sum of the first (p+q) terms of the given AP
=p+q2[2a+(p+q1)d]

=p+q2[(1pq)d+(p+q1)d]=0

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Formula for Sum of N Terms of an AP
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon