# PreCalculus Name: Chapter 11 Test

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```PreCalculus
Chapter 11 Test
Name:
Directions: Show all work and reasoning to receive full credit.
Write out the first four terms of the sequence.
3n 
n 1 

1) a n  (1) 
 (n  3)! 
2) a1  3 and an  3an1  4
4 16 64
4096
3) Express the sum using summation notation:      
.
5 10 15
30
Determine the nth term for the following sequences.
4) 2, 1, 4, 7, 10
2 2 2 2
5) 2, , , ,
3 9 27 81
6) Arithmetic: 6th term is -10; 15th term is -46
Using concepts learned during this unit, determine the sum of the following sequences.
7) 7  14  28  56  112    1,835, 008
8) 20 
37
31
 17   14    (43)
2
2
9) A theater has 24 rows with 23 seats in the first row, 28 in the second row, 33 in the third row, and so forth.
How many seats are in the theater?
Find the sum of each of the infinite geometric series.
5 5
10) 5    
3 9


 2
11)
4 
 3
k 3
k 1
12) Initially, a pendulum swings through an arc of 3 feet. On each successive swing, the length of the arc is
80% of the previous length. How far will it swing altogether before coming to a complete stop?
13) Use mathematical induction to prove the statement is true for all positive integers n.
6  2  6  3  6    6n  3n(n  1)
14) Expand the expression using the Binomial Theorem and simplify.
 2 x  3 y 4
```