Q) If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p + q – n).
Ans: We know that nth term of an A.P. = a + (n-1) d
Therefore, pth term Tp = a + (p – 1) x d = q
Similarly, qth term Tq = a + (q – 1) x d = p
By solving these two equations from each other, we get:
pd – qd = q – p
d = -1
Hence, value of a = q – (p – 1) (-1)
a = p + q – 1
Hence, nth term of this AP is = a + (n – 1) d
= (p + q – 1) + (n -1) (-1)
= p + q – 1 – n + 1
= p + q – n ……………. Hence Proved