Question

if p arithmetic means are inserted between a nad b ,prove that d=b-a/p+1

Answer 1

mightbe something akin to this

let pn = {p1,p2,p3,p4,...,pn}

p1 = (a+p2)/2

p2 = (p1+p3)/2
= (a+p2+p3)/2

p3 = (p2 + p4)/2
= (a+p2+p3+p4)/2

...

pn = (a+p2+p3+p4+...+pn+b)/2

2pn = a+p2+p3+p4+...+pn+b

2pn - pn = a+p2+p3+p4+...+p{n-1}+b

pn(2 - 1) = a+p2+p3+p4+...+p{n-1}+b

pn = a+p2+p3+p4+...+p{n-1}+b

Answer 2

but then maybe not :/