S. If pth term of an AP. is g and the gth term is p,thenits rth term i

1.	S. If pth term of an AP. is g and the gth term is p,thenits rth term is :
Answer» Let first term be a and common difference be d. pth term = a + (p-1)d = q -----(i) qth term = a+ (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 - 1 Hence, rth term = a + (r-1)d = q + p -1 + (r-1)(-1) = q + p -1 + r +1 = p + q - r

S. If pth term of an AP. is g and the gth term is p,thenits rth term is :

Answer»

Let first term be a and common difference be d.

pth term = a + (p-1)d = q -----(i)

qth term = a+ (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 - 1

Hence,

rth term = a + (r-1)d = q + p -1 + (r-1)(-1) = q + p -1 + r +1 = p + q - r