设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
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![设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.](/uploads/image/z/13942522-10-2.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E5%B7%B2%E7%9F%A5a2%3D6%2C6a1%2Ba3%3D30%2C%E6%B1%82an%E5%92%8CSn.)
设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
A2=6 A1q=6
6A1+A3 6A1+A1q²=30
q/(6+q²)=1/5
q²-5q+6=0
a=2或q=3
当q=2时,A1=3,则:An=A1q^(n-1)=3×2^(n-1)
Sn=[A1(1-q^n)]/[1-q]=3[2^(n)-1]
当q=3时,A1=2,则An=A1q^(n-1)=2×3^(n-1)
Sn=[A1(1-q^n)]/[1-q]=3^n-1