设Sn为等差数列{an}的前n项和,若S3=3,S6=24,则a9多少?还有一题：已知各项均为正数的等比数列｛an｝,a1a2a3=5,a7a8a9=10,则a4a5a6等于多少?

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设Sn为等差数列{an}的前n项和,若S3=3,S6=24,则a9多少?
还有一题：已知各项均为正数的等比数列｛an｝,a1a2a3=5,a7a8a9=10,则a4a5a6等于多少?

设首项为a1,公差为d
s3=a1+a2+a3
=a1+(a1+d)+(a1+2d)
=3a1+3d
s6=s3+a4+a5+a6
=3a1+3d+(a1+3d)+(a1+4d)+(a1+5d)
=6a1+15d
3a1+3d=3
6a1+15d=24
a1=-1,d=2
a9=a1+8d=15
设首项为a1,公比为q
a1a2a3=a1(a1q)(a1q^2)=a1^3q^3
a7a8a9=(a1q^6)(a1q^7)(a1q^8)=a1^3q^21
(a1a2a3)(a7a8a9)=a1^6q^24=5*10=50
a1^3q^12=√50
a4a5a6=(a1q^3)(a1q^4)(a1q^5)=a1^3q^12=√50

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