搜狗做题网Sequences and Series (001)
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Sequences and Series (001)
If the first,fifth and tenth terms of an arithmetic progression are in geometric progression and the sum of the second and eighth terms is 20,find the first term and the (non-zero) common difference.
If the first,fifth and tenth terms of an arithmetic progression are in geometric progression and the sum of the second and eighth terms is 20,find the first term and the (non-zero) common difference.
Solution:let the geometric progression a、a+4d and a+9d.
∴q^2=(1+4d/a)^2=1+9d/a.
∴d/a=1/16,or d/a=-1/16.
When d/a=-1/16,it is not to fit this question .
So d/a=1/16.
∴ a=16d.
∵(a+q)+(a+7q)=20
∴a+4d=10
∵20d=10
∴d=1/2
∴ a=8
∴q^2=(1+4d/a)^2=1+9d/a.
∴d/a=1/16,or d/a=-1/16.
When d/a=-1/16,it is not to fit this question .
So d/a=1/16.
∴ a=16d.
∵(a+q)+(a+7q)=20
∴a+4d=10
∵20d=10
∴d=1/2
∴ a=8
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