Question

if the mth term of ap is m and nth is m then what mthn term

Answer 1

Answer:

here is ur answer

Step-by-step explanation:

mth term = n

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

nth term=m

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

Subtracting (1) from (2)

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

a+nd-d - (a+md-d) = m-n

a+nd-d-a-md+d =m-n

nd-md = m-n

-d(m-n) = m-n

d= -1.........(3)

Substituting (3)in (1)

a+(m-1)-1 = n

a-m+1 = n

a= m+n-1........(4)

Now finding rth term:

a+(r-1)d

Substituting (3) and (4)

m+n-1 + (r-1)-1

m+n-1-r+1

= m+n-r

Solved!

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Step-by-step explanation:

Answer 2

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.

Step-by-step explanation: