已知等差數(shù)列{
an}的首項
a1=1,公差
d>0,且第二項,第五項,第十四項分別是等比數(shù)列{
bn}的第二項,第三項,第四項.
(1)求數(shù)列{
an}與{
bn}的通項公式;
(2)設(shè)數(shù)列{
cn}對任意自然數(shù)
n,均有
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,
求
c1+
c2+
c3+……+
c2006值.
(1)
an=2
n-1,
bn=3
n-1;
(2)
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(1)由題意得(
a1+
d)(
a1+13
d)=(
a1+4
d)
2(
d>0) 解得
d=2,∴
an=2
n-1,
bn=3
n-1.
(2)當(dāng)
n=1時,
c1="3" 當(dāng)
n≥2時,
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,
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
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="1,"
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=
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(
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