Question

the mth term AP is n and nth term is m.The r th term of it is
A. M+n+r
B. N+m-2r
C. M+n+r/2
D. None of these

Answer 1

Answer - Option (D) - None of these

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

Given that mth term of an AP is n.

Tm = a + (n - 1) * d

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



Given that nth term of an AP is m.

Tn = a + (n - 1) * d

m = a + (n - 1) * d     ------------------- (2)


Now,

On solving (1) & (2), we get

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

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

md - nd = n - m

d(m - n) = n - m

d = n - m/m - n

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

d = -1.


Substitute d = -1 in (2), we get

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

m = a - n + 1

a = m + n - 1.


Now,

Rth term tr = a + (r - 1) * d

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

                   = m + n - 1 - r + 1

                   = m + n - r.


Therefore the rth term = m + n - r.


Hope this helps!