If AM between pth and qth terms of an AP be equal to the AM between rth and sth terms of the AP then prove that p+q =r +s

Question

parthkohli · Answer

lol, simple proof

parthkohli · Answer

what is the expression for AM between two numbers?

anonymous · Answer

Sorry I managed prove lol , it was simple

anonymous · Answer

It is not that formula , chuck that

parthkohli · Answer

...?$$\dfrac{a_p + a_q}{2}=\dfrac{a_{r} + a_s }{2}$$$$\implies a_p + a_q = a_r + a_s$$$$\implies a + (p-1)d = a + (q-1)d = a + (r-1)d + a + (s-1)d$$Yup.

anonymous · Answer

Yes yes , all will cancel out 
and p+q=r+s

Since i was doing n means , i read it as AM's

parthkohli · Answer

OK, no problem!

I studied sequences and series a few weeks ago at coaching, so feel free to tag me.  I haven't practiced this for a few days.  :)

anonymous · Answer

Ok , sure