Name: ___________________________
Date: _________________________
PRECALC TEST – POLAR COORD AND SEQUENCES AND SERIES
Arithmetic Sequences & Series
nth term : an  a1  (n 1)d
n
1
n
Geometric Sequences & Series
n
Sum: sn 
1
1
(1 r)
1. What is the 12th term in the sequence {1, 3, 5, 7,…}?
a. 22
b. 23
c.24
D 25
2. What is the sum of the first 6 terms of the series 2+10+50+…?
a. 3,906
B 7,812
C 15,624
D 31,248
3. A child puts $1.00 into a piggy bank. One week later, he puts $1.25 inthe bank. Two weeks
later, he puts $1.50 in the bank, and so on. Howmuch money does he put in the bank on the
25th week?
a.
$ 6.25
B $7.00
C $93.00
D $100.00
Part II. Solve. Show all your work.
1. Find the rectangular coordinates for each of the following polar coordinates:
 5 
a.  4, 
 6 
2 

b.  8, 
3 

2. Given the rectangular coordinates below, find the polar coordinates satisfying the
conditions given:
a. 3,3 ; r  0 and 0    2
3. Plot the following:
 7 
A.  6, 
 6 
3 

B.  3, 
4 

C. 8, 
5 

D.   6, 
3 

11 

E.   5,

6 

2 

F.   4, 
3 



b.  5,5 3 ; r  0 and      
4. Find the next four terms of each sequence and write the equation for the nth term.
a. 35, 32, 29, 26, …
b. 6, 18, 54 …
_____ , _____ , _____ , _____
______, _____, ______, _____
a n = ______________
a n = ______________
5. Given the explicit formula for the sequence, find the first five terms and the named term in
the problem.
an 
a.
a23
11 1
 (n  1)
8 2
_____ , _____ , _____ , _____ , _____
= _________
b.
a18
an  3n1
_____ , _____ , _____ , _____ , _____
= _________
6. Given the first term and the common difference of an arithmetic sequence find the first five
terms and the explicit formula.
a.
an
a1  28, d  10
_____ , _____ , _____ , _____ , _____
= _________
7. Given a term and the common difference of an arithmetic sequence find the first five terms
and the explicit formula.
a.
an
a38  53.2, d  1.1
_____ , _____ , _____ , _____ , _____
= _________
8. Given the first term and the common ratio of a geometric sequence find the first five terms
and the explicit formula.
a.
an
a1  1, r  2
_____ , _____ , _____ , _____ , _____
= _________
9. Given a term and the common ratio of a geometric sequence find the first five terms and the
explicit formula.
a.
an
a5  
16
2
,r
27
3
_____ , _____ , _____ , _____ , _____
= _________
10. Find the first five terms using the given recursive formula
a1  1.2
a.
an  (an1 ) 2  0.9
11. Evaluate each series.
8
a.
4 (n  3) 2
n 3
6
b.
 2(.5)
n 1
n 1
12. Graph the polar equation:
r  3  3sin
_____ , _____ , _____ , _____ , _____