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Let \(a_1, a_2, a_3,\dots\) be an increasing arithmetic sequence of integers. If \(a_4a_5 = 13\), what is\( a_3a_6\)?

 Jan 17, 2019
 #1
avatar+104069 
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The only way that    a4 * a5   = 13     is if   a4 = 1   and a5 = 13

 

So....d  =  12

 

So  a3 =  (a4 - d)    and a6 = ( a5 + d)

 

So

 

a3 * a6   =

 

(a4 - d ) ( a5 + d)  =    ( 1 - 12) ( 13 + 12)  = (-11) (25)  =  -275

 

 

cool cool cool

 Jan 17, 2019

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