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The Diavik Diamond Mine is located on East Island in Lac de Gras East, Northwest Territories. The diamonds that are extracted from the mine were brought to surface when the kimberlite rock erupted 55 million years ago. In 2003, the first production year of the mine, 3.8 million carats were produced. Suppose the life expectancy of the mine is 20 years, and the number of diamond carats expected to be extracted from the mine in the 20th year is 113.2 million carets. If the extraction of diamonds produces an arithmetic sequence, determine:

 

a. the common difference

 

b. what this value means

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 May 1, 2020
 #1
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a1  =  3.8  = the first term

 

a20 = 113.2  =the 20th term

 

So......

 

To find the common difference, d,  we have

 

a20   =   a1  + d ( 20 - 1)            filling in the blanks we have

 

113.2 =  3.8 + d (19)      subtract 3.8 from both sides

 

109.4  = d (19)    divide both sides by 19

 

d = 547/95   

 

For the second part...."d"  tells us  that the  number of carets (in millions)  is increasing by  547/95 ≈ 5.8 million carets per year  

 

 

cool cool cool

 May 1, 2020

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