450 students have enrolled in the creative writing course over 10 years
Solution:
Given that,
The first year the course = 9 students enrolled
The second year of course = 17 students enrolled
The third year of course = 25 students
To find: total number of students that will have enrolled in the creative writing course over 10 years
Assuming this trend continues:
9, 17, 25
Find the difference between terms
17 - 9 = 8
25 - 17 = 8
Thus the difference between terms remains constant
This forms a Arithmetic sequence with common difference 8
Thus, we can find the students enrolled in successive years by adding 8
First year = 9
second year = 9 + 8 = 17
third year = 17 + 8 = 25
fourth year = 25 + 8 = 33
fifth year = 33 + 8 = 41
sixth year = 41 + 8 = 49
seventh year = 49 + 8 = 57
eight year = 57 + 8 = 65
ninth year = 65 + 8 = 73
tenth year = 73 + 8 = 81
Total number of students over 10 years = 9 + 17 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81
Total number of students over 10 years = 450
Thus 450 students have enrolled in the creative writing course over 10 years