Question

In an AP if mth term is 'n' and the nth term is 'm' where m=n, find that p th term.​

Answer 1

Correct Question:

In an AP if mth term is 'n' and the nth term is 'm' where m ≠ n, find the pth term.

Answer:-

Given:

mth term of an AP = n

nth term = m

We know that,

nth term of an AP – a(n) = a + (n - 1)d

So,

⟹ a(m) = a + (m - 1)d = n

⟹ a + md - d = n

⟹ a = n - md + d -- equation (1)

Similarly,

⟹ a(n) = a + (n - 1)d = m

Substitute the value of a from equation (1).

⟹ n - md + d + nd - d = m

⟹ n - m = md - nd

⟹ (n - m) = - d(n - m)

⟹ 1 = - d

⟹ d = - 1

Substitute the value of d in equation (1).

⟹ a = n - m( - 1) + ( - 1)

⟹ a = n + m - 1

Now,

⟶ a(p) = a + (p - 1)d

Putting the values of a & d we get,

⟶ a(p) = n + m - 1 + (p - 1) * ( - 1)

⟹ a(p) = n + m - 1 - p + 1

⟹ a(p) = m + n - p

Therefore, the pth term of the given AP is m + n - p.