If the sum of first p terms of an A.P. is equal to the sum of the firs

1.	If the sum of first p terms of an A.P. is equal to the sum of the first g terms, thenfind the sum of the first (p + 9) terms.
Answer» Sp=Sq p/2[2a +(p-1)d]=q/2 [2a+(q-1)d] p[2a +pd - d]=q[2a+qd - d ] 2ap + p^2d - pd =2aq + q^2d -qd 2ap-2aq +p^2d -q^2d -pd +qd =0 2a (p-q) +(p+q)(p-q)d -d(p-q)=0 (p-q)[2a + (p+q)d - d ]=0 2a + (p+q)d - d=0 2a + [(p+q)-1]d=0

If the sum of first p terms of an A.P. is equal to the sum of the first g terms, thenfind the sum of the first (p + 9) terms.

Answer»

Sp=Sq

p/2[2a +(p-1)d]=q/2 [2a+(q-1)d]

p[2a +pd - d]=q[2a+qd - d ]

2ap + p^2d - pd =2aq + q^2d -qd

2ap-2aq +p^2d -q^2d -pd +qd =0

2a (p-q) +(p+q)(p-q)d -d(p-q)=0

(p-q)[2a + (p+q)d - d ]=0

2a + (p+q)d - d=0

2a + [(p+q)-1]d=0