Question

Attention Brainliest answers wanted persons,
the mth term of an AP be 1/n and its nth term be 1/m, then show that its mnth term is 1.
best answer according to me will be marked as Brainliest​

Answer 1

Answer:

given that, mth term=1/n and nth term=1/m.

then ,let a and d be the first term and the common difference of the A.P.

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

subtracting equation (1) by (2) we get,

md-d-nd+d=1/n-1/m

=>d(m-n)=m-n/mn

=>d=1/mn.

again if we put this value in equation (1) or (2) we get, a=1/mn.

then, let A be the mnth term of the AP

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

hence proved.

HOpe iT HelP YOu DEaR

Answer 2

Answer:

mnth term = 1

Step-by-step explanation:

Condition 1 :

mth term of an AP = 1/n.

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

Condition 2 :

nth term of an AP = 1/m.

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

Combine (1) - (2) to proceed further.

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

=> (m - 1) * d - (n - 1) * d = 1/n - 1/m

=> md - d - nd + d = 1/n - 1/m

=> (m - n) * d = 1/n - 1/m

=> (m - n) * d = (m - n)/mn

=> d = 1/mn     ------ (3)

We got common difference also. Place d in (2)

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

=> a + n/mn - 1/mn = 1/m

=> a + 1/m - 1/mn = 1/m

=>  a = 1/mn

Now, we have to find mnth term.

=> amn = a + (mn - 1) * d

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

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

           = 1.

Hence, mnth term = 1.

#Hope my answer helped you!