Question

The mth term of an A. P. is n and nth term is m. The rth term of it is
(a) m +n +r
(b) n + m - 2
(c) m + n +r/2
(d) m+n- r ​

Answer 1

Answer :

d) m+n-r

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!

Answer 2

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!

Step-by-step explanation: