Question

if in an arithmetic progression the mean of the pth and qth term is equal to mean of rth term and sth term then prove that p + q = r + s​

Answer 1

Answer:

please click a images and see your answer you did not understand I will write.

Step-by-step explanation:

A.M between p

th

term and q

th

term = A.M between r

th

term and s

th

term of the A.P.

Let 'a' be first term of A.P and 'd' be common difference.

p

th

term =a+(p−1)d

q

th

term =a+(q−1)d

r

th

term =a+(r−1)d

s

th

term =a+(s−1)d



2

a+(p−1)d+a+(q−1)d

=



2

a+(r−1)d+a+(s−1)d



2a+(p+q)d−



2d=



2a+(r+s)d−



2d

p+q=r+s.