数列{an}是等差数列,若m+n=r+s(m,n,r,s∈N*),则下列等式恒成立的是( )A.am+an=ar+asB.am•an=ar•asC.am-an
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数列{an}是等差数列,若m+n=r+s(m,n,r,s∈N*),则下列等式恒成立的是( )A.am+an=ar+as | B.am•an=ar•as | C.am-an=ar-as | D.am•ar=an•as |
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答案
∵数列{an}是等差数列, ∴am+an=[a1+(m-1)d]+[a1+(n-1)d]=2a1+(m+n-2)d, ar+as=[a1+(r-1)d]+[a1+(s-1)d]=2a1+(r+s-2)d, 又m+n=r+s(m,n,r,s∈N*), 则am+an=ar+as. 故选A |
举一反三
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