Question

If the mth term of an ap be 1/n and its nth term be 1/m then show that its (mn)th terms is 1

Answer 1

Answer:

amn=1

Step-by-step explanation:

Let a be the first term and d be the common difference.

mth term of an A.P is 1/m

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

a+md-d=1/n ----->(1)

nth term of an A.P is 1/n

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

a+nd-d=1/m ------>(2)

subtract 2 from 1.

we get

d=1/mn

put d=1/mn in Equation 1

we get

a=1/mn

to find mnth term

amn=a+(mn-1)d

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

finally we get

amn=1