Arithmetic and Geometric Word Problems
We can find the nth term and a sum, but how does this apply to real life? 
1.
Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 22 seats
in the second row, 24 seats in the third row, and so on.
2. Consider a job offer with a starting salary of $32,500 and an annual raise of $2,500. Determine the total
compensation from the company through six full years of employment.
3. An investment firm has a job opening with a salary of $30,000 for the first year. Suppose that during the next 30
years there is a 5% raise each year. Find the total compensation of the 40-year period.
4.
You have a job that starts out with a salary of $30,000. You have two options: 1) a 5% increase in your salary per
year or 2) a $3000 raise each year. Which option would you choose? Explain.
Extra Practice
1) Is the sequence arithmetic, geometric, or neither? Find the 6th term.
a. 1, 4, 9, 16, …
b. 40, 20, 10, 5, …
c. 2, 5, 9, 14, …
2) Write a formula for the nth term.
a.
2 3 4 5
, , , ,...
9 16 25 36
b. 40, 20, 10, 5, …
d. 6, 14, 22, 30, …
c. 6, 14, 22, 30, …
3) Write the formula for the nth term. Then find a30
a. -4, 0, 4, 8, 12, …
b. 1, 2, 4, 8, …
c. 8, 12, 18, 27, … (hint: part c is geometric)
4) Write the series using summation notation.
a. 600  300 150  75  37.5
b. 1  4  7  10  ...  298
5) Find the first term of the sequence using the given information.
a. Arithmetic: a4  10
a16  46
b. Geometric: a3  32
a10  4096
6) Find the sum of the sequence. (hint: are the rules are arithmetic or geometric?)
1
b.   
n 1  3 
8
105
a.
  3n  4 
n 1
n 1
7) Find the sum of the infinite geometric sequence.
a. 8, 12, 18, 27, …
b. 40, 20, 10, 5, …
c.
1 5 25
, , ,...
2 4 8
d.
4 3 9
,1, , ,...
3 4 16