if the sum m term ap is same as the sum of its n term show that the sum of m+m term is zero

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if the sum m term ap is same as the sum of its n term show that the sum of m+m term is zero

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jayram singh 17th Jul, 2018

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Answer (1)

Ratula 26th Aug, 2018

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

m(2a+(m-1)d)=n(2a+(n-1)d)

2am+dm^2-md=2an+dn^2-nd

2a(m-n)+d(m^2-n^2)-d(m-n)=0

(m-n)(2a+dm+dn-d)=0

m=n

or

2a+d(m+n-1)=0

As m not equal to n,

2a+d(m+n-1)=0

so

(m+n)/2(2a+(m+n-1)d)=0

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