014. If the mth term of an AP isand the n term isthen show that its (m

1.	014. If the mth term of an AP isand the n term isthen show that its (mn)th term is 171
Answer» Am=1/nAn=1/m a+(m-1)d=1/n.........(1)a+(n-1)d=1/m.........(2) eqⁿ(2) - eqⁿ(1) (n-m)d=1/m - 1/nd=1/mn put in eqⁿ 1a+(m-1)(1/mn)=1/na+1/n -1/mn=1/na-1/mn=0a=1/mn Amn=a+(mn-1)dAmn=1/mn +(mn-1)1/mnAmn=1/mn+1-1/mnAmn=1

014. If the mth term of an AP isand the n term isthen show that its (mn)th term is 171

Answer»

Am=1/nAn=1/m

a+(m-1)d=1/n.........(1)a+(n-1)d=1/m.........(2)

eqⁿ(2) - eqⁿ(1)

(n-m)d=1/m - 1/nd=1/mn

put in eqⁿ 1a+(m-1)(1/mn)=1/na+1/n -1/mn=1/na-1/mn=0a=1/mn

Amn=a+(mn-1)dAmn=1/mn +(mn-1)1/mnAmn=1/mn+1-1/mnAmn=1