(1)在等比数列an中,已知a4a7=-512,a3+a8=124,且公比为整数,求a10.(2)在等比数列an中,有a3a11=4a7,数列bn是等差数列,且b7=a7.求b5+b9.(3)在等比数列an中,若a1a2a3a4=1,a13a14a15a16=8求a41a42a43a44

Question

(1)在等比数列an中,已知a4a7=-512,a3+a8=124,且公比为整数,求a10.(2) 在等比数列an中,有a3a11=4a7,数列bn是等差数列,且b7=a7.求b5+b9.(3) 在等比数列an中,若a1a2a3a4=1,a13a14a15a16=8求a41a42a43a44

Answer 1

解:a4a7=a3a8=-512.
a3+a8=124 q为整数
求得a3=-4 a8=128 q=-2
a10=a8×4=512
(2)a3a11=a7a7=4a7
∴a7=4=b7
b5+b9=2b7=8
(3)a1a2a3a4=1
a13a14a15a16=a1a2a3a4q(48)=8
求得q(48)=8
∴a41a42a43a44
=a13a14a15a16q(112)
=8×8×8×2
=1024
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