Question

If the mth term of an ap is 1/p and its pth term is 1/m then show that its mpth term is 1

Answer 1

Given ,m th term of A.P is 1/p
1/p =a+(m-1)d --> eq(1)
p th term of A.P is 1/m
1/m=a+(p-1)d --> eq(2)

(1)-(2)
1/p = a+(m-1)d
1/m=a+(p-1)d

1/p - 1/m =( m-1)d - (p-1)d

m-p/mp=(m-p)d

1/mp=d

mp=d

From eq(1)

1/p=a+(m-1)/mp

a= m-(m-1)/mp

a=1/mp

mp th term of A.P = a+ (mp-1)d
= 1/mp+ (mp-1)mp
=1/mp+1-1/mp
=1

Hence proved that mp th term is 1 .