Question

if p times th p th term of an AP is equal to q times the qth term .show that it's (p+q) th term is zero​

Answer 1

Answer:

pth= a+( p-1)d

qth = a+(q-1)d

(p+q)= a+ (p+q-1)d=?

as p×pth=q×qth

p(a+(p-1)d)= q{a+ (q-1)d}

a(p-q)= d(q^2-p^2-q+p)

a= d{ (q+p)(q-p)+ (q-p)}/p-q

=d(-q-p+1)

substituting it in 3rd we have

d(p+q-1) - (p+q-1)d =0