Question

The mth term of an A. P. is n and the nth term is m. Show that its (m+n)th term is zero.

Answer 1

Let a be the first term and d be the common difference of given AP

Now, mth term = a + (m - 1) d which is equals to n

∴ a + ( m - 1 )d = n ----- ( i )

nth terms = m

∴a + ( n - 1)d = m ---- (ii)

Subtracting ( ii ) from ( i )

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

d [ (m - 1) - (n - 1)] = n - m

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

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

dividing both sides by ( m - n)

d = - 1

Putting value of d in ( i )

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

a - m + 1 = n

a = n + m - 1

Now

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

Putting values of a and d

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

n + m - 1 - m - n + 1

= 0

(m + n)th term = 0

Answer 2

Answer:

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