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Question

If the sum of m terms of an AP is the same as the sum of its n terms. The sum of its (m + n) terms is

A
0
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B
1
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C
m+n2
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D
mn
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Solution

The correct option is A 0

Sm=Sn

Sm=m2(2a+(m1)d)

Sn=n2[2a+(n1)d]

SmSn=m2(2a+(m1)d)n2[2a+(n1)d]=0

SmSn=(mn)(2a+(m+n1)d)=0

Therefore (2a+(m+n1)d)=0

SmSn=2a(mn)+m(m1)dn(n1)d=0

Sm+n=m+n2(2a+((m+n)1)d)

2a[mn]+d[m(m1)n(n1)]=0

2a[mn]+d[m2mn2+n]=0

(mn)[2a+(m+n1)d]=0

Sm+n=0

Option is A



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