Question

(b) If mth and nth term of an A.P. are 1/n and 1/m respectively, then find its
mnth
term.
​

Answer 1

Answer:

mnth term=2-mn/mn

Step-by-step explanation:

tm=1/n

tn=1/m

tm=a+(m-1)d

tn=a+(n-1)d

1/n=a+(m-1)d

a=1/n+dm-d

1/m=a+(n-1)d

a=1/m+dn-d

1/n+dm-d=1/m+dn-d

1+dmn-dn/n=1+dmn-dm/m

m+dm²n-dmn=n+dmn²-dmn---- cross multiplication

m+dm²n=n+dmn²

dm²n-dmn²=n-m

dmn(m-n)=n-m

dmn=-1

d=-1/mn.

a=1/n+dm-d

a=1/n-1/mn(m-1)

a=1/n-(m-1)/mn

a=m-(m-1)/mn

a=1/mn.

mnth term=a+(mn-1)d

=1/mn+(mn-1)-1/mn

=1-mn+1/mn

= 2-mn/mn.

HOPE THIS HELPS!