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The product of the first five terms of a geometric progression is 1024, and the fourth term is 2017. Find the second term.

 Jan 24, 2021
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Call the first term, N

Let the common ratio  be , r

 

So

Nr^3   =  2017

N    =      2017  / r^3

 

So  we  have  that

 

( 2017/r^3) ( 2017/r^2) ( 2017/r) (2017) (2107 r)  =  1024   simplify

 

(2017)^5  / r^5   = 1024

 

(2017)^5  /1024  =   r^5               take the 5th root of both sides

 

2017/4   = r

 

The second term  is

 

First term * r  = 

 

 [ 2017 / ( (2017/4)^3 ]  *  (2017/4)    =    16/2017

 

 

cool cool cool

 Jan 24, 2021
edited by CPhill  Jan 24, 2021

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