Question

If the anthmetic mean between the pth and qth terms of an AP is equal to the Arithmetic mean
between the rth and sth terms of the AP, then show that p +q=r+s.​

Answer 1

Answer:

Step-by-step explanation:

Let first term=a and common difference=d

Then pth term=a+(p-1)d

pth term=a+(q-1)d

mean=1/2](a+(p-1)d+a+(q-1)d)]=1/2[2a+(p+q-2)d]

similarily mean of rth and sth term

=1/2(2a+(r+s-2)d]

given

1/2[2a+(p+q-2)d] = 1/2(2a+(r+s-2)d]

2a+(p+q-2)d=2a+(r+s-2)d

(p+q-2)d=(r+s-2)d

p+q-2=r=s-2

p+q=r+s

Proved