MATH 4 REVIEW SHEET FOR UNIT 2 TEST ON SEQUENCES AND SERIES
ARITHMETIC SEQUENCES
GEOMETRIC SEQUENCES
𝑑 = 𝑎𝑛 − 𝑎𝑛−1
Explicit: 𝑎𝑛 = 𝑎1 + 𝑑(𝑛 − 1)
Recursive: 𝑎𝑛 = 𝑎𝑛−1 + 𝑑
𝑛
Finite Sum 1: 𝑆𝑛 = (𝑎1 + 𝑎𝑛 )
𝑎𝑛
𝑎2 𝑎3
=
=
𝑎𝑛−1 𝑎1 𝑎2
Explicit: 𝑎𝑛 = 𝑎1 (𝑟)𝑛−1
Recursive: 𝑎𝑛 = (𝑎𝑛−1 ) ∙ (𝑟)
𝑟=
2
Finite Sum: 𝑆𝑛 = 𝑎1 ∙ (
1−𝑟 𝑛
1−𝑟
)
Find the first 4 terms of each sequence
1)
an  n1.5  1
__________, __________, __________, __________,
2)
an  (3) 0.5 n
__________, __________, __________, __________,
3)
an  2n  1
__________, __________, __________, __________,
4)
an  an1  2 with a1=1
__________, __________, __________, __________,
Find the 5th term using the given sequence formula
5) 𝑎𝑛 = 𝑛2
6) 𝑎𝑛 = 1.5𝑎𝑛−1
5th term = ___________________
5th term = _____________________
Where 𝑎1 = 1
7) 𝑎𝑛 = 𝑛0.8 + 3
8) 𝑎𝑛 = 5 + 𝑎𝑛−1
5th term = ___________________
5th term = _____________________
Where 𝑎1 = 1
Identify the type of sequence and make the appropriate choice: A=arithmetic, G=geometric, N=neither. For Arithmetic or
geometric, find “d” or “r”, as appropriate. If “d” or “r” does not exist, write DNE.
9)
10)
11)
12)
{5, 2, −1, … }
{−1, 2, −4, … }
{4, 8, 12, … }
{3, 13.5, 60.75, … }
A
A
A
A
G
G
G
G
N
N
N
N
d or r = _____________
d or r = _____________
d or r = _____________
d or r = _____________
Use the following arithmetic sequence for the next 3 questions: {𝟐, 𝟒, 𝟔, … }
13) Find the common difference: d = ________
14) Find the explicit arithmetic formula: ____________________
15) Find the recursive arithmetic formula: ______________________
Use the following sequence for the next 3 questions: {𝟏, 𝟐, 𝟒, … }
16) Find the common ratio: r=________
17) Find the explicit geometric formula: ____________________
18) Find the recursive geometric formula: ______________________
Use the following arithmetic sequence for the next 3 questions: {−𝟓, −𝟒, −𝟑, … }
19) Find the common difference: d = ________
20) Find the explicit arithmetic formula: ____________________
21) Find the recursive arithmetic formula: ______________________
Use the following sequence for the next 3 questions: {−𝟏, 𝟐, −𝟒 … }
22) Find the common ratio: r =________
23) Find the explicit geometric formula: ____________________
24) Find the recursive geometric formula: ______________________
25) Find the 15th finite sum of this finite arithmetic sequence
S15 = ____________________
26) Find the 15th finite sum of this finite geometric sequence
S15 = ____________________
27) Find the 15th finite sum of this finite arithmetic sequence
S15 = ____________________
28) Find the 15th finite sum of this finite geometric sequence
S15 = ____________________
Find the arithmetic finite sum in 29,30, 31
29) n= 15, a1=3, and a15=65
30) ∑20
𝑛=1 4𝑛 + 5
31) ∑15
𝑛=1 2𝑛 − 3
Find the geometric finite sum in 32,33,34
32) n=7, r=-3, a1=2
33) ∑8𝑛=1 −3(2)𝑛−1
𝑛−1
34) ∑11
𝑛=1(−2)
1 , 2 , 3 , ... , 15
1 , 2 , 4 , ... 
1 , 3 , 5 , ... , 29
1 , 3 , 9 , ... 