Math, asked by khushbooVeerwani, 5 months ago

The sum of P terms of an ap is Q and the sum of Q terms is P.Find the sum of( P + Q )terms ​

Answers

Answered by Anonymous
7

Solution :-

According to the question,

The sum of P terms of an AP is Q and the sum of Q terms is P

As we know that,

Sn = n/2 ( 2a + ( n - 1 )d)

Now, Sum of p terms = q

Sp = p/2 ( 2a + ( p - 1 )d ) = q. eq( 1 )

Sum of Q terms = P

Sq = q/2 ( 2a + ( q - 1 )d) = p. eq( 2)

Now,

Sum of p + q terms

S(p + q) = p + q / 2 * ( 2a + ( p + q - 1 )d) eq( 3 )

From ( 1 ) and ( 2 ) equation we get,

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

= 2a + ( p - 1 )d = 2q/p. eq( 4 )

and,

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

= 2a + ( q - 1 )d = 2p/q. eq( 5 )

Now,

Subtracting ( 4 ) and ( 5 )

2p/q - 2q/p = ( q - p)d

By taking LCM

= 2 ( p + q ) ( p - q ) / pq = ( q - p)d

= d = -2 ( p + q) / pq

Now, Take eq( 3 )

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

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

Subsitute the value of d

= p + q /2 ( 2q /p + q ( - 2 ( q + p) / qp)

= p + q /2 ( 2q - 2q - 2q / p)

= - ( p + q ) .

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