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Let a_1, a_2, a_3 be an arithmetic sequence. If a_4/a_2 = 2, find a_5/a_3.

 Feb 2, 2022
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a_1, a_2, a_3, ... can also be written as a_1, a_1 + d, a_1 + 2d... where d is the common difference of the sequence.

 

a_4/a_2 = (a_1 + 3d)/(a_1 + d) = 2

 

a_1 + 3d = 2a_1 + 2d

d = a_1

 

a_5/a_3 = (a_1 + 4d)/(a_1 + 2d)

= 5d/3d

5/3

 Feb 2, 2022
edited by CubeyThePenguin  Feb 2, 2022

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