if pth term of an AP is q and qth term of an AP is p then prove that its nth term is p+q-1

if pth term of an AP is q and qth term of an AP is p then prove that i

1.	if pth term of an AP is q and qth term of an AP is p then prove that its nth term is p+q-1
Answer» \xa0Let first term be a and common difference be d.pth term = a + (p-1)d = q -----(i)qth term = a\xa0+ (q-1)d = p -----(ii)(ii) - (i) gives(q - p)d = p - q or d = -1(i) gives a = q - (p-1)d = q - (p-1)(-1) = q + p - 1Hence,nth term = a + (n-1)d= q + p -1 + (n-1)(-1)= q + p -1 + n +1= p + q - n