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
+128406 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
