Mathematics 2200
Sequences and Series
Unit Assignment
Name:________________
Section 1: Selected Response
Circle the letter of the correct answer.
1.
What is the general term of the sequence {19, 9, -1, -11, ...}
A) tn=10n+9
2.
C) -48.75
D) 5
B) 37
C) 43
D) 55
B) 6j + 4k
C) 3k – 2j
D) 2k + j
B) 1
C) -3
D) 9
B) 644
C) 3381
D)
The general term of the sequences is given by the formula tn = 500(0.8)n – 1. Which represents
this sequence?
A) 500, 400, 300, ..
9.
B) 14.75
What is the sum of the series where t1= , d = 8 and n = 21?
A)
8.
D)
If an arithmetic sequence has t3 = -3 and t8 = -18, what is the value of t1?
A) 3
7.
C)
The third term of an arithmetic sequence is j and the fourth term is k. What is the sixth term?
A) j + k
6.
?
What is the tenth term of an arithmetic sequence if t2=11 and t6=27?
A) 31
5.
B)
D) tn= -10n + 9
In the formula for the general term of an arithmetic sequence tn = 5 + (n – 1)(-9.75), what is
the common difference?
A) -9.75
4.
C) tn= -10n + 29
What is the general term for the sequence {
A)
3.
B) tn = -10n + 19
B) 500, 400, 320, ...
C) 400, 320, 240, ...
D) 400, 320, 256, ...
How many terms are in the sequence {5, 10, 20, 40 , 80, ..., 81 290} ?
A) 13
B) 14
C) 15
D) 16
10.
What is the sum of the geometric series 5 + 2.5 + 1.25 + ...+ 0.3125?
A)
11.
D)
C) 121 943
B) The series is
convergent and has a
sum of .
D) 120 023
?
C) The series is
divergent and has no
sum.
D) The series is
divergent and has a
sum of .
The sum of an infinite geometric series is 8 and the first term is 14. What is the common ratio
of the series?
A)
14.
B) 2 082 800
Which best describes the series
A) The series is
convergent and has no
sum.
13.
C)
The population of a community was 82 000 at the beginning of 2000. Assuming a growth rate
of 1.6% per year since 2000, what will the population be at the beginning of 2025?
A) 123 894
12.
B)
B)
C)
D)
C) 27-36+48-64 ...
D) 48+24+0+ ...
Which is a convergent geometric series?
A) 48+36+27+ ...
B) 27+36+48+...
Section 2: Constructed Response
Answer all questions in the space provided showing all work.
1.
In an arithmetic sequence, t3= 7x -5, t4=2x + 4 and tn = x + 1
A)
Determine the value of x
B)
Write the general term of the sequence.
2.
In the arithmetic sequence, t7 = 13 and S9=63. Determine the first term and common
difference and write the general term.
3.
At the end of the second week after opening a new fitness club has 870 members. At the end
of the seventh week there are 1110. Suppose the increase is arithmetic.
A)
How many members joined the club each week?
B)
4.
How many members were there in the first week?
For a geometric sequence t4= 4x + 8 and t7= x – 4. If the common ratio is , what is the first
term?
5.
The first three terms of a geometric sequence are t1 = x – 1, t2 = 3x +1 and t3 = 9x + 23.
Determine the value of x and write the general term of the sequence.
6.
Calculate S12 for the sequence {1000, -800, 640, ...}
7.
In a geometric sequence t1 = -3, r = 2, and tn = -786 432, determine the number of terms?
8.
In an infinite geometric sequence, the second term is
and the fifth term is 1. Determine t1
and r and determine the sum of the corresponding geometric series.