1.在等比数列{a}中,前几项和为Sn(1)a7=12,q=根号2开3次方,求a19（2）a2=-2,a5=54,求a8
3个回答
1、解1)∵a7=a1*q^6=12,
a19=a1*q^18=a1*q^6*q^12
=12*[√2^(1/3)]^18=12*2^3=12*8=96
2)a2=a1q=-2,a5=a1*q^4=54
q^3=-27,∴q=-3,a1=2/3
∴a8=a1*q^7=2/3*(-3)^7=-1458
3)a9*a10=a1*a18
∴a18=a9*a10/a1=100/5=20
4)∵S3+S6=2S9
∴ a1(1-q^2)/(1-q)+a1*(1-q^5)/(1-q)
=2a1(1-q^8)/(1-q)
即1-q^2+1-q^5=2-2*q^8
q^2*(2q^6-q^3-1)=0
q^3=1,q^3=-1/2
q=0,q=1,舍去
∴q=(-1/2)^(1/3)
2、∵a4=a1*q^3=1/8,a1=1,
∴q^3=1/8,q=1/2,
∴S10=a1*(1-q^9)/(1-q)
=1*[1-（1/2）^9]/(1-1/2)
=511/256
1）∵bn=log2(an),得b1=log2(8)=3
∴bn-b(n-1)=log2(an)-log2[a(n-1)]
=log2[an/a(n-1)]=log2(q)=定值
则{bn}是首项a1=3,公差d=log2(q)的等差数列
2）、由上可知
Sn=nb1+[n(n-1)log2(q)]/2
=3n+[n(n-1)log2(q)]/2
S6=18+15log2(q),S7=21+21log2(q)
S8=24+28log2(q)
∵S7＞S6,S7＞S8,
∴21+21*log2(q)＞18+15log2(q),
21+21*log2(q)＞24+28log2(q)
即-1/2＜log2(q)＜-3/7
∴√2/2＜q＜2^(-3/7)
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