IB MATH STUDIES
Ms. Polecka
Name: ______________________________________
Date: ______________
Period: _________
ARITHMETIC SEQUENCES
un  u1  d(n 1)
1. List the first five terms of the sequence:
a. {2n}
b. {2n +11}
c. { 2 n }
d. { 15  (2) n }



2. Consider the following sequence: 6, 17, 28, 39, 50 , . . .
a. Show that the sequence is arithmetic.
b. Find the formula for its general term un

c. Find its 50th term.
d. Is 325 a member?
e. Is 761 a member?
3. Consider the following sequence: 87, 83, 79, 75, . . .
a. Show that the sequence is arithmetic.
b. Find the formula for its general term un

c. Find its 40th term.
d. Is -143 a member?
4. A sequence is defined by: un  3n  2
a. Show that the sequence is arithmetic.
b. Find u1 and d.


c. Find its 57th term.
5. A sequence is defined by un 
71  7n
2
a. Show that the sequence is arithmetic.
b. Find u1 and d.
c. Find u75



6. Find k given the consecutive arithmetic terms:
a.
32, k, 3
b.
k, 7, 10
c.
d.
k – 1, 2k +3, 7 – k
e.
k, k 2 , k 2  6
f.
 
k + 1, 2k +1, 13
5, k, k 2  8

7. Find the general term un for an arithmetic sequence given that:
a. u7  41 and u13  77
b. u5  2 and u12  12





1
2
c. u7 1 and u15  39


IB MATH STUDIES
Ms. Polecka
Name: ______________________________________
Date: ______________
Period: _________
GEOMETRIC SEQUENCES
un  u1r n 1
1. For the geometric sequence with the first two terms given, find b and c:
a. 2, 6, b, c, …

b. 10 ,5, b, c, …
c. 12, - 6, b, c, …
2. Given the sequence 5, 10, 20, 40, …
b. Find un the 15th term.
a. Show that the sequence is geometric.

3. Given the sequence 12, -6, 3, -1.5, …
a. Show that the sequence is geometric.
b. Find un the 13th term. (as a fraction)

4. Show the sequence 8, -6, 4.5, -3.375, … is geometric and hence find the 10th term as a decimal.
5. Find k given that the following are consecutive terms of a geometric sequence.
a. 7, k, 28
b. k, 3k, 20-k
c. k, k+8, 9k
6. Find the general term un of the geometric sequence which has u4  24 and u7 192



7. . Find the general term un of the geometric sequence which has u3  8 and u6  1



8. . Find the general term un of the geometric sequence which has u7  24 and u15  384




IB MATH STUDIES
Ms. Polecka
Name: ______________________________________
Date: ______________
Period: _________
ARITHMETIC & GEOMETRIC SERIES
Arithmetic Series
Geometric Series
u1(r n 1)
u1(1  r n )
Sn 
S

or
n
r 1
1 r
n
n
Sn  (u1  un ) or Sn  (2u1  (n 1)d)
2
2
 + 9 + 13 + 17 + 21 + 25
1. Find 1+5
a. by simply adding



n
2
r 1
b. using Sn  (u1  un )
c. using Sn 


n
(2u1  (n 1)d)
2
2. Find the sum of:
a. 3 + 7 + 11 +15 + … to 20 terms
b. ½ + 3 + 5 ½ + 8 + … to 50 terms
c. 100 + 93 + 86 + 79 +… to 40 terms
d. 50 + 48 ½ + 47 + 45 ½ + … to 80 terms
3. Find the sum of:
a. 5 + 8 + 11 +14 + … + 101
b. 50 + 49 ½ + 49 + 48 ½ + … + ( - 20 )
4. An arithmetic series has seven terms. The first term is 5 and the last term is 53.
Find the sum of the series.
5. Each section of a soccer stadium has 44 rows with 22 seats in the first row, 23 seats in the
second row, 24 seats in the third row, and so on.
How many seats are there in row 44?
How many seats are there in a section?
6. Find the sum of the following series:
a. 12 + 6 + 3 + 1.5 + … to 10 terms
b. 6 – 3 +1 ½ - ¾ + … to 12 terms
c. 3 + 9 + 15 + 21 + … to 23 terms
d. 24 + 12 +6 +3 + … to 12 terms