Question

If mth term is n amd nth n term is m show that its rth term is (m +n-r

Answer 1

EXPLANATION.

• GIVEN

mth term is equal to = n

nth term is equal to = m

show that it's rth term is ( m + n - r).

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

Nth term = a + ( n - 1 ) d = m ....... (2)

From equation (1) and (2) we get,

( m - n) d = n - m

d = -1

put the value of d = -1 in equation (1)

we get,

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

a + ( - m + 1 ) = n

a - m + 1 = n

a = n + m - 1

From Rth term = a + ( r - 1 ) d

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

n + m - 1 - r + 1

n + m - r

Hence proved