Question-41966

Question Number 41966 by Raj Singh last updated on 16/Aug/18

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Aug/18

S_{p} = \frac{p}{2} [2 a + (p - 1) d]

S_{Q} = \frac{Q}{2} [2 a + (Q - 1) d]

g i v e n S_{p} = S_{Q}

\frac{p}{2} [2 a + (p - 1) d] = \frac{Q}{2} [2 a + (Q - 1) d]

2 p a + (p^{2} - p) d - 2 Q a - (Q^{2} - Q) d = 0

2 a (P - Q) + d (P^{2} - P - Q^{2} + Q) = 0

2 a (P - Q) + d {(P + Q) (P - Q) - (P - Q)} = 0

2 a (P - Q) + (P - Q) {P + Q - 1} d = 0

2 a + (P + Q - 1) d = 0

n o s S_{P + Q} = \frac{P + Q}{2} [2 a + (P + Q - 1) d]

= \frac{P + Q}{2} \times 0 = 0