Question

若等差數(shù)列{a_n}與等比數(shù)列{b_n}的首項是相等的正數(shù)，且它們的第2n+1項也相等，則有（　�。�

A．a(chǎn)n+1＜bn+1

B．a(chǎn)n+1≤bn+1

C．a(chǎn)n+1≥bn+1

D．a(chǎn)n+1＞bn+1

Answer 1

因為等差數(shù)列{a_n}和等比數(shù)列{b_n}各項都是正數(shù)，且a₁=b₁，a_2n+1=b_2n+1，
所以a_n+1-b_n+1=

a1+a2n+1

2

-

b1•b2n+1

=

a1+a2n+1-2 a1•a2n+1

2

=

( a1 - a2n+1 ) 2

2

≥0．
即 a_n+1≥b_n+1．
故選C．