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

Answer 1

S
$sum \: of \: p \: \: terms = m \\ sum \: of \: q \: terms = m \\ sum \: pof \: p \: terms = sum \: of \: q \: terms$
By applying formula
Sp=Sq
p/2(2a+(p-1)d)=q/2(2a+(q-1)d)
2 to 2 cancel.
p(2a+(p-1)d)=q(2a+(q-1)d)
{2ap+(p^2-p)pd}-{2aq+(q^2-q)qd}
2a(p-q) + (p^2-q^2) - (p-q)d = 0
(p-q) 2a + (p+q-1)d = 0
Dividing and multiplying both side by p-q
Solve it and u will get ur answer which is
sum of p+q terms = 0
Hope it will help u.
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