Chapter 9.4-9.5 Review AATS
NAME______________
9.4 Arithmetic Series
1. What is the sum of the odd integers from 1 to 231?
2. What is the sum of the finite arithmetic series 3+7+11+15+19+…+99?
3. The Guitar Center has an alternative bonus plan. It pays a $1000 bonus if a new
sales person makes 8 sales in the first week and then improves by two sales per week
each week thereafter. One salesperson qualified for this bonus with the minimum
number of sales. How many sales did the person make in week 42? In all 42 weeks?
4. What is the summation notation for the series?
a) -4 + 3 + 10 + 17 + … + 262 + 269
b) 2 + -3 + -8 + -13 + … + -73 + -78
5. What is the sum of the first sixteen terms of the arithmetic sequence
1, 5, 9, 13, ... ?
Complete the following summations.
45
6.
 (2n  3)
n 1
6
7.
 (n
2
 2n)
n 1
9.5 Geometric Series
8. Suppose you go to work and for a salary you told your boss you would work for one
penny on the first day, 3 cents for the second day, 9 cents on the third day and so on for
15 days.
a) What sequence is this?
b) What is the explicit formula?
c) How much would you get paid on the 15th day? (In dollars)
d) Over 15 days, how much would you get paid? (In dollars)
9. What is the sum of the finite geometric series?
a) 2 + 8+ 32 + … + 32,768
b) 4 + 12 + 36 + … + 8748
10.What is the sum of the finite geometric series?
12
 4   3
n 1
n 1
11. Determine whether each series is arithmetic or geometric. Then evaluate the finite
series for the specified number of terms.
a) 3 + 5 + 7 +…. ; n = 75
b) 128 – 64 + 32 – 16 + … ; n = 30
12. Determine whether each infinite geometric series diverges or converges. If the
series converges, state r and the sum.
1 1 1
1
  
a) 1   
3 9 27 81
b) 1.2 + .12 + .012 + …
Converge or Diverge_________
Converge or Diverge_________
r= _______________________
r= _______________________
Sum=_____________________
Sum=_____________________
c) 3 + 9 + 27 + …
Converge or Diverge_________
Sum=_____________________
r= _______________________
13. Evaluate each infinite series that has a sum.

a.
1

 
n 1  3 
n 1
a1 ? a2 ? r ? S?

1
b.  2  
n 1  4 
n 1
14. The height of the ball bounces is less than the previous bounce due to friction. The
heights of the bounces form a geometric sequence. Suppose the ball is dropped from
one meter and rebounds to 95% of the height of the previous bounce. What is the total
distance traveled by the ball when it comes to rest?