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Help 11

 Mar 19, 2018
 #1
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11) The common ratio should be - 5. So, you would have the sequence of:

37, - 185, 925, - 4,625........etc.

 

12)

N=(L - F) / D + 1, where N=Number of terms, L=Last term, F=First term, D = Common difference

N=(65 - (-5)) / 5 +1

N = 15 - Number of terms

Sum = (F + L) / 2 x N 

Sum = (-5 + 65) / 2 x 15 

Sum = (60) / 2 x 15

Sum = 450

 Mar 19, 2018
 #2
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+1

GP      37, ...   925

 

925/37=25

 

So the common ratio must be a factor of the form    25 to the power of some number

The obvious ones to try are    \(\pm25\;\;or\;\; \pm5\)

 

-185/37 = -5    could be that one

-4625/37 = -125 = (-5)^3  or that one

 

 

-925/37 = -25  = (-5)^2   or that one, no that cannot work, just by inspection.

481/37 = 13    not that one

 

 

 

37,    37*-5,    37*-5*-5,.....

37,    -185,         925,     -4625,  

 

so there are two answers and both have the common ratio of  -5

 Mar 19, 2018

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