Question

a) If the pth term of an arithmetic progression is q and
the gth term is p, show that its (p + q) th term is 0.

Answer 1

hi friend ,


given pth term of an AP is q


let a be the first term and d be the common difference of given AP


then we know that

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

and also given qth term is p


p=a+(q-1)d--------(2)


by (1)-(2), we get


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

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

=d=-1


by substituting the value of d in (1) we get,


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

=a=p+q-1



now the (p+q)th term will be



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


hence proved




i hope this will help u ;)