in an arithmetic progression, the sum of p terms is m and the sum of q terms is also m.Find the sum of (p+q) terms

Question

in an arithmetic progression, the sum of p terms is m and  the sum of q terms is also m.Find the sum of (p+q) terms

hartnn · Answer

know the formula for sum of 'n' terms ?

wwe123 · Answer

yes

hartnn · Answer

did u try to equate sum of p and sum of q terms...

wwe123 · Answer

yes

hartnn · Answer

did the factor of p-q cancel out ?

hartnn · Answer

and is the answer = 0 ??

wwe123 · Answer

answer is 0 ,but how to show ,i am not able to do...

hartnn · Answer

p[2a+(p-1)d]= q[2a+(q-1)d]
did u get this ?

hartnn · Answer

this u get if u know the formula.

wwe123 · Answer

yes, i know the formua
 but (p+q) ??

hartnn · Answer

did u expand that ?

hartnn · Answer

what u got ?

wwe123 · Answer

1 min

hartnn · Answer

there is a factor of p-q which gets cancelled.

wwe123 · Answer

how to expand and solve  @hartnn

hartnn · Answer

p[2a+(p-1)d]= q[2a+(q-1)d]
2ap + p(p-1)d = 2aq + q(q-1)d 
2a(p-q) = d[q(q-1)-p(p-1)]
did u get this? 
want to try further ?

hartnn · Answer

u get p-q on right side also.

hartnn · Answer

did u get or should i continue ?

wwe123 · Answer

plz continue, i am stunk

hartnn · Answer

its simple algebra..... 
2a(p-q) = d[q(q-1)-p(p-1)]
2a(p-q) = d[q^2-q-p^2+p]
2a(p-q) = d[q^2-p^2 -(q-p]
2a(p-q) = d(q-p)[q+p-1]
2a(p-q) =- d(p-q)[q+p-1]
we can cancel p-q because p-q is not 0, because p not =q
2a + (p+q-1)d = 0

hartnn · Answer

i hope u can do the last step....

wwe123 · Answer

NOW
sum upto (p+q) terms = (p+q)/2(2a+(p+q-1)d)
                                 =(p+q)/2(2a-2a)   
                                 =0
is this right @hartnn

hartnn · Answer

yes. good :)

hartnn · Answer

clear with all steps ?

wwe123 · Answer

thanks :)

hartnn · Answer

welcome ^_^