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

If the pth term of an A.P. is q and the qth term is p, prove that the nth term is equal to (p+qn).

Open in App
Solution

We know that the formula for the nth term is tn=a+(n1)d, where a is the first term, d is the common difference.

It is given that the pth term of an A.P is q and qth term of an A.P is p, therefore,

q=a+(p1)d.........(1)
p=a+(q1)d.........(2)

Subtract equation 2 from 1 as follows:

(aa)+[(p1)d(q1)d]=qpd(p1q+1)=qpd(pq)=(pq)d=(pq)(pq)=1

Substitute the value of common difference d in equation 1:

q=a+(p1)(1)q=ap+1a=q+p1

Now, the nth term with a=q+p1 and d=1 can be obtained as follows:

tn=a+(n1)d=q+p1+(n1)(1)=q+p1n+1=p+qn

Hence, the nth term is (p+qn).


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Nature of Roots
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon