Question

If (p + q)^th term of an A.P. is m and (p - q)^th term is n, then pth term is ______.

Options

• mn

• mn

• `sqrt(mn)`

• `sqrt(mn)`

• `1/2(m-n)`

• `1/2(m-n)`

• `1/2(m+n)`

• `1/2(m+n)`

Answer 1

If (p + q)^th term of an A.P. is m and (p - q)^th term is n, then pth term is `underline(1/2(m+n))`.

Explanation:-

Let a is first term and d is common difference

∴ a_{p + q} = m

a_{p - q} = n

⇒ a + (p + q - 1)d = m    …(i)

⇒ a + (p - q - 1)d = n     …(ii)

On adding (i) and (ii), we get

2a + (2p - 2)d = m + n

⇒ a + (p - 1)d = `(m+n)/2`     …[Dividing by 2]

∴ a_n = `(m+n)/2`

Answer 2

If (p + q)^th term of an A.P. is m and (p - q)^th term is n, then pth term is `underline(1/2(m+n))`.

Explanation:-

Let a is first term and d is common difference

∴ a_{p + q} = m

a_{p - q} = n

⇒ a + (p + q - 1)d = m    …(i)

⇒ a + (p - q - 1)d = n     …(ii)

On adding (i) and (ii), we get

2a + (2p - 2)d = m + n

⇒ a + (p - 1)d = `(m+n)/2`     …[Dividing by 2]

∴ a_n = `(m+n)/2`