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The sequence $6,-9,x,y$ is such that the first three terms form an arithmetic sequence and the last three terms form a geometric sequence. Find $x$ and $y$.

Express your answer as $x,y$.

 

There is no 6 terms, so assuming that 6 is the first term we know x = -34, now what would y be if it is now geometric?

 Feb 18, 2019
 #1
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Well, one possibility would be:

 

6, - 9, -24, -64

The first 3 form an arithmetic sequence with -15 as the common difference, and the last 3 form a geometric sequence with a common ratio of 2 2/3.

 Feb 18, 2019
 #2
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The common difference is    -9 - 6 =    - 15

 

So...the third term would need to be - 24

 

The common ratio between the second and third terms  is    (-24) /(-9) =  8/ 3

 

So....the fourth term is    - 24 ( 8/3)  = -64

 

So....the series is

 

6 , -9, -24, -64

 

 

cool cool cool

 Feb 18, 2019

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