The number of students enrolling in a creative writing course during the summer months increases each year. The first year the course was offered, 9 students enrolled. In the second year, 17 students enrolled and in the third year 25 students enrolled. What is the total number of students that will have enrolled in the creative writing course over 10 years, assuming this trend continues?

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