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A.P

Posted June 3rd, 2009 by alpha
in

In an A.P whose first term is 0a , the sum of first p terms is 0 . Show that the sum of next q terms is
$ \frac{-a(p+q)}{p-1} $

‹ Quadratic equation Prove that ›

Comments

My method

On June 4th, 2009 alpha says:

According to the question
$ a_1,a_2,a_3,a_4....................a_p,a_(p+1),.....................a_(p+q) $
So, there are (p+q)terms in total.
$ s_p=0 $
$ s_q=s_(p+q)-s_p $
$ s_q=s_(p+q) $

on solving it further i got
$ 2pqd+2pd-qd+2aq+q^2d=0 $

How to reach to the answer?

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Please check my procedure.

On June 6th, 2009 alpha says:

````Maths````
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answer

On June 6th, 2009 Structure says:
$$a_1=a$$
$$a_2=a+r$$
$$a_p=a+(p-1)r$$
$$s_p=a_1+a_2+ ...+a_p=pa+r(1+2+...+(p-1))=pa+\frac{rp(p-1)}{2}=0$$
$$r=-\frac{2a}{p-1}$$
$$s_{p+q}-s_p=s_{p+q}=\frac{a_1+a_{p+q}}{2}(p+q)=\frac{a+a+(p+q-1)r}{2}(p+q)=-\frac{aq(p+q)}{p-1}$$

~~THANK YOU ~~

On June 6th, 2009 alpha says:

````Maths````
000
(((())))
///

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