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设等差数列an的前n项和为Sn若a2a4a6a8=120且1/(a4a6a8)+1/(a2a6a8)+1/(a2a4a8)+1/(a2a4a6)=7/60则S9=
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设等差数列an的前n项和为Sn 若a2a4a6a8=120 且1/(a4a6a8)+1/(a2a6a8)+1/(a2a4a8)+1/(a2a4a6)=7/60 则S9=
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答案和解析
an = a1+(n-1)d
1/(a4a6a8)+1/(a2a6a8)+1/(a2a4a8)+1/(a2a4a6) =7/60
(1/120)(a2+a4+a6+a8) =7/60
a2+a4+a6+a8 = 14
4a1+16d=14
a1+4d =7/2 (1)
S9 = (a1+4d)9
= (7/2)9
=63/2
1/(a4a6a8)+1/(a2a6a8)+1/(a2a4a8)+1/(a2a4a6) =7/60
(1/120)(a2+a4+a6+a8) =7/60
a2+a4+a6+a8 = 14
4a1+16d=14
a1+4d =7/2 (1)
S9 = (a1+4d)9
= (7/2)9
=63/2
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