已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}通项公式an;若sn=93,求n

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已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}通项公式an;若sn=93,求n已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}

已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}通项公式an;若sn=93,求n
已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}通项公式an;若sn=93,求n

已知等比数列{an}满足a3=12,a8=3/8,记其前n项和为sn,求数列{an}通项公式an;若sn=93,求n
由a3=12=,a8=3/8;可知q=1/2;a1=48
所以:数列{an}通项公式an=48q^(n-1)
sn=93=a1(1-q^n)/(1-q)=48[1-1/(2^n)]/(1-1/2)
则:n=5

比数列通式an=a1*q^(n-1),比较a3=12,a8=3/8可知q^5=a8/a3=(3/8)/12=1/32,
得q=1/2,a1=a3/(q^2)=12/(<1/2>^2)=48,
所以,通式an=48*(1/2)^(n-1);
再根据求和sn=a1(-1)/(q-1)
代入得93=48*(<1/2>^n-1)/(<1/2>-1)可求得n=5