Question

If the p th term of an ap is q and its q th term is p then show that its (p+q) th term is zero

Answer 1

ap of pth term =q
a+(p-1)d=q.........EQ 1
ap of qth term =p
a+(q-1)d=p........ EQ 2
subtract EQ 2 from EQ 1
p-q = a+(q-1)d - a+(p-1)d
p-q=(q-1)d -(p-1)d
p-q=qd-d-pd+d
p-q=qd-pd
p-q=(q-p)d
p-q=-(p-q)d
d=p-q/ -(p/q)
d=-1...... EQ A
ap of p+qth term
a+(p+q-1)d= a+(pd+qd-d)
=a+(pd-d)+qd
=a+(p-1)d+qd
=q+qd from EQ 1
=q+q(-1) from EQ A
=q-q
=0