Question

The mthterm of an

a.P. Is n and the nthterm is m. Find the rthterm of the

a.P

Answer 1

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Answer 2

In an A.P, an = a + (n - 1)d

→ am = n = a + (m - 1)d _(i)

→ an = m = a + (n - 1)d _(ii)

Now, (ii) - (i) we get,

→ m - n = a + (n - 1)d - a - (m - 1)d

→ m - n = (n - 1)d + (1 - m)d

→ m - n = d(n - 1 + 1 - m)

→ m - n = - d(m - n)

→ - 1 = d

Substituting value in (i),

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

→ a = m + n - 1

Now, then rth term will be

→ ar = a + (r - 1)d

→ ar = (m + n - 1) + (r - 1)(-1)

→ ar = m + n - 1 - r + 1

→ ar = m + n - r