MATH 4 REVIEW SHEET FOR UNIT 2 TEST ON SEQUENCES AND

```MATH 4 REVIEW SHEET FOR UNIT 2 TEST ON SEQUENCES AND SERIES
ARITHMETIC SEQUENCES
GEOMETRIC SEQUENCES
π = ππ − ππ−1
Explicit: ππ = π1 + π(π − 1)
Recursive: ππ = ππ−1 + π
π
Finite Sum 1: ππ = (π1 + ππ )
ππ
π2 π3
=
=
ππ−1 π1 π2
Explicit: ππ = π1 (π)π−1
Recursive: ππ = (ππ−1 ) β (π)
π=
2
Finite Sum: ππ = π1 β (
1−π π
1−π
)
Find the first 4 terms of each sequence
1)
an ο½ n1.5 ο­ 1
__________, __________, __________, __________,
2)
an ο½ (3) 0.5 n
__________, __________, __________, __________,
3)
an ο½ 2n ο­ 1
__________, __________, __________, __________,
4)
an ο½ anο­1 ο« 2 with a1=1
__________, __________, __________, __________,
Find the 5th term using the given sequence formula
5) ππ = π2
6) ππ = 1.5ππ−1
5th term = ___________________
5th term = _____________________
Where π1 = 1
7) ππ = π0.8 + 3
8) ππ = 5 + ππ−1
5th term = ___________________
5th term = _____________________
Where π1 = 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: {π, π, π, … }
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: {π, π, π, … }
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: {−π, −π, −π, … }
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: {−π, π, −π … }
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
π=1 4π + 5
31) ∑15
π=1 2π − 3
Find the geometric finite sum in 32,33,34
32) n=7, r=-3, a1=2
33) ∑8π=1 −3(2)π−1
π−1
34) ∑11
π=1(−2)
ο»1 , 2 , 3 , ... , 15ο½
ο»1 , 2 , 4 , ... ο½
ο»1 , 3 , 5 , ... , 29ο½
ο»1 , 3 , 9 , ... ο½
```