PreCalculus
Midterm Review of Ch 11
Name:
Use separate paper to complete these review exercises. Show all work!
1. An auditorium has 20 rows of seats. There are 20 seats in the first row, 21
seats in the second row, 22 seats in the third row, and so on. The last row has
39 seats. How many seats are there in all 20 rows?
2.
A brick patio has the approximate shape of a trapezoid. The patio has 18 rows
of bricks. The first row has 14 bricks and the 18th row has 31 bricks. How
many bricks are in the patio?
12
3. Find the sum:
 4(0.3)
n
n 1
6. This year’s Monopoly tournament has 625 participants. The rules of the
tournament state 5 players must begin a game, and only the winner of each game
advances to the next round of competition. Write a sequence for the number of
games played in each round. Is this arithmetic or geometric? Finite or infinite?
How many rounds are need to crown a champion? What is the series related to
your sequence? What is the sum of this series? What does this value represent?
7. Evaluate the sum of the whole numbers from 1-30.
6
8. Evaluate:
 500(1.04)
n
n 0
9. Write an explicit formula for a n for the following sequence
330 , 336.6 , 343.332 , 350.19864, …
10. On Sunday, Mr. Mierzwa notices a 1 cm crack in his windshield. Each day the crack
spreads an additional 0.5 cm. Write the first 6 terms of the sequence that models this
situation. How long is the crack after two weeks?
11.
Each tone of a musical scale vibrates at a certain frequency, in Hertz (Hz), or
cycles per second. The frequency of middle A is 440 Hz, and each time you
move up one half-step, the frequency is multiplied by 1.06.
a. Complete the list of frequencies of the next three half-steps above middle A.
440 , ______ , _______ , _______
b. Write an explicit formula for the sequence in part a.
Evaluate:
8
12.
 (3n  2)
n 1
100
13.
n
n 1
14.
  1  n 1 

20    
n 1
  2 
15.
How would you express the sum of the first 25 perfect squares in Sigma Notation?
16.
Can the series 3 + 3 + 3 + 3 + … + 3 be classified as arithmetic? Why or why not? Could
this series be classified as geometric? Explain why or why not.
17.
A Las Vegas casino is hosting a Poker Tournament. The rules state a game must begin
with 7 players and only the winner advances to the next round. Suppose 2,401 players
enter the tournament.
7
a. Write a sequence for the number of games played in each round of the
tournament.
b. Write the series that is related to the sequence in part a.
c. Write the series from part c. in Sigma notation, then evaluate the sum. Show
work! What does this sum represent? (Relate your answer to the context of the
problem.)
d. How many rounds are needed to complete the tournament?