This document contains examples of arithmetic and geometric sequence word problems. Example 1 involves a radio contest where the prize increases by $150 each day until someone answers correctly, asking what the prize will be if no one answers correctly until Friday. Example 2 asks what someone's salary would be after two months if their paycheck started at $100 per week and doubled every week. Example 3 asks how many seats are in the 20th row of an auditorium where each row has 3 more seats than the previous row, starting with 20 seats in the first row.

1. Arithmetic and
Geometric Sequence
WORD PROBLEMS

2. Example 1
Every day a radio station asks a question
for a prize of $150. If the 5th caller
does not answer correctly, the prize
money increased by $150 each day
until someone correctly answers their
question.

3. What will be the prize if the
contest starts on Monday
and no one answers
correctly until friday.

4. Example 2
What if your pay check
started at $100 a week and
doubled every week. What
would your salary be after two
months?

5. Example 3
An auditorium has 20 rows of seats. There are 20 seats in the first
row, 23 seats in the second row, 26 seats in the third row, and so on.
How many seats are there in 20th row?
1 20 1 19d c   

6. Example 4
. A small business sells $10,000 worth of sports materials during its first
year. The owner of the business has set a goal of increasing annual sales
by $7500 each year for 20 years. Assuming that the goal is met, find the
sales during the 20th year this business is in operation.

7. Example 4
. A small business sells $10,000 worth of sports materials during its first
year. The owner of the business has set a goal of increasing annual sales
by $7500 each year for 20 years. Assuming that the goal is met, find the
sales during the 20th years this business is in operation.

8. Shown in the table is the
growth of red blood cells
per minutes. Assuming
this trend continues what
will be the number of cells
in 12 minutes ?
Example 5
Minutes No. of cells
1 250
2 500
3 1000

9. Upon injecting a patient
with an anti-virus
Vaccine the number of
bacteria decreases per
minute. If the trend in the
table continues, what
number of minutes before
the bacteria will be totally
gone?
Example 6
Minutes No. of
bacteria in
the cells
1 9,000
2 3,000
3 1,000

10. As shown in the table, the monthly
rent of an apartment depends on the
number of bedrooms. If the pattern is
extended, What is the likely
cost of a 8 bedroom
apartment?
Example 5
Bedrooms Cost
1 $ 550
2 $ 625
3 $ 700

11. Find the next three terms of 2, 3, 9/2, ___, ___, ___
3 – 2 vs. 9/2 – 3… not arithmetic
3 9/ 2 3
1.5 geometric r
2 3 2
    
3 3 3 3 3 3
2 2 2
9
2, 3, , , ,
2
9 9 9
2 2 2 2 2 2
     
9
2, 3, , ,
27 81 243
4 8
,
2 16

12. 1 9
1 2
If a ,r , find a .
2 3
 
1a First term
na nth term
nS sum of n terms
n number of terms
r commonratio
1/2
x
9
NA
2/3
n 1
n 1a a r 

9 1
1 2
x
2 3

  
   
  
8
8
2
x
2 3


7
8
2
3

128
6561


13. 9Find a of 2, 2, 2 2,...
1a First term
na nth term
nS sum of n terms
n number of terms
r commonratio
x
9
NA
2
2 2 2
r 2
22
  
n 1
n 1a a r 

 
9 1
x 2 2


 
8
x 2 2
x 16 2