设等比数列an的前n项和为Sn,若S4=8,S8=20,则 a9+a10+a11+a12=?
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![设等比数列an的前n项和为Sn,若S4=8,S8=20,则 a9+a10+a11+a12=?](/uploads/image/z/15109805-29-5.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E8%8B%A5S4%3D8%2CS8%3D20%2C%E5%88%99+a9%2Ba10%2Ba11%2Ba12%3D%3F)
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设等比数列an的前n项和为Sn,若S4=8,S8=20,则 a9+a10+a11+a12=?
设等比数列an的前n项和为Sn,若S4=8,S8=20,则 a9+a10+a11+a12=?
设等比数列an的前n项和为Sn,若S4=8,S8=20,则 a9+a10+a11+a12=?
an为等比数列,则S4,S8-S4,S12-S8也成等比数列
证明:S4=a1+a2+a3+a4
S8-S4=a5+a6+a7+a8
S12-S8=a9+a10+a11+a12
(S8-S4)/S4=q=(S12-S8)/(S8-S4)
所以,S4,S8-S4,S12-S8成等比数列
所以,(S8-S4)^2=S4*(S12-S8)
所以,S12-S8=a9+a10+a11+a12=18
中英切换也繁,打字母符号也繁,不看功劳看苦劳啊~
(S8-S4):S4=(S12-S8):(S8-S4)
S12-S8=a9+a10+a11+a12=18