Question

In: Math

If the pth term of an AP is q and the qth term is p, prove that its nth term is (p + q - n).

Expert Solution

• pth term = q

• q th term = p

a +(p – 1) d = q______(1)

a +(q – 1) d = p______(2)

Subtracting equation (2) – (1), we get

a +(q – 1) d – [a +(p – 1) d] = p – q

a + dq – d – a – pd – + d = p – q

dq – dp = p – q

d(q – p) = -(q – p)

d = -1

Putting d= -1 in equation (1)

a +(p – 1) d = q

a + (p – 1)(-1) = q

a – p + 1 = q

a = p + q – 1

Thus,

nth term = a + (n – 1)d

nth term = (p + q – 1) + (n – 1) × (-1)

nth term = (p + q – n)

Nikhil Thakur answered 2 years ago

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