SOLUTION: The 2nd, 4th and 8th terms of an arithmetic progression are the three consecutive terms of a geometric progression and the 11th term of an arithmetric progression is 22.
i) Find
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i) Find
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Question 1177532: The 2nd, 4th and 8th terms of an arithmetic progression are the three consecutive terms of a geometric progression and the 11th term of an arithmetric progression is 22.
i) Find the first term and common difference if the arithmetic progression
ii) What is the common ratio of the geometric progression Answer by mananth(16946) (Show Source):
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a+d , a+3d , a+7d
(a+3d)/(a+d) = (a+7d)/(a+3d)
(a+3d)^2 = (a+d)(a+7d)
a^2 +6ad +9d^2 = a^2+7ad +ad +7d^2
2ad-2d^2 =0
2d(a-d)=0
a=d.
a+10d =22
a=d
11d=22
d=2, a=2
Ratio
(a+7d)/(a+3d)= 16/8 =2
