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Algebra II: Quiz 1 - Sequences Flashcards | StudBud
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Algebra II: Quiz 1 - Sequences
Algebra II: Quiz 1 - Sequences
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For Ms. McKennie's Algebra II class at Butler College Prep; extra credit with proof of completion!
Flashcards
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Questions
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Answers
1
The first five terms of a geometric sequence are 3, 9, 27, 81, 243. What is the common ratio of this sequence?
3
9
4
2
2
In an arithmetic sequence, S(n), S(4)=5 and S(6)=29. What is S(12)-S(10)? SYW
S\left(12\right)-S\left(10\right)=12
S\left(12\right)-S\left(10\right)=15
S\left(12\right)-S\left(10\right)=36
S\left(12\right)-S\left(10\right)=24
3
Identify the explicit formula for an arithmetic sequence.
a_n=a_1+(n-1)d
a_n=a_{n-1}+d
a_n=a_1\cdot r^{n-1}
a_n=a_{_{n-1}}\cdot r
4
Write a recursive definition the sequence.
Q(1)=3;Q(n)=\frac{1}{2}\cdot Q(n-1)+2;for→n\ge2
\left(Q(1)=3;Q(n)=2\cdot Q(n-1\right)+2;for→n\ge2
Q(1)=3;Q(n)=Q(n-1+2.5;for→n\ge2
Q(1)=3;Q(n)=Q(n-1)\times2.5;for→n\ge2
5
What are the two minimum requirements for a recursive definition of a sequence?
f(1)
a(n)=a(n-1)\cdot r→OR-\backslash+d,OR-\backslash+nOR-\backslash+n^2
the first term & the recursive equation
what you divide by
6
Identify the general term or explicit formula for a geometric sequence.
a_n=a_{_{n-1}}\cdot r
a_n=a_1\cdot r^{n-1}
a_n=a_{n-1}+d
a_n=a_1+(n-1)d
7
A term is...
a number in a sequence
the first number in a series
the length of time served
a condition of a contract
8
Describe a recursive process in words to determine the term in the sequence given by 2, 6, 10, 14, 18, ...
a(n) = a(n-1) x 4
a(1)=2, a(n) = a(n-1) + 4
times by 4
add 4 to each term
9
What is the formula to find the common difference?
d=t_1-t_2
d=\frac{t_2}{t_1}
d=t_2-t_1
d=\frac{t_1}{t_2}
10
Identify the recursive formula to find the next term in a geometric sequence.
a_n=a_1\cdot r^{n-1}
a_n=a_{n-1}+d
a_n=a_{_{n-1}}\cdot r
a_n=a_1+(n-1)d
11
Which formula defines the sequence f(1)=2, f(2)=6, f(3)=10, f(4)=14, f(5)=18? SYW
f(1)=2,f(n)=f(n-1)+6for→n\ge2
f(1)=2,f(n)=f(n-1)+4for→n\ge2
f(1)=6,f(n)=f(n-1)+4for→n\ge2
f(1)=2,f(n)=f(n-1)+2for→n\ge2
12
What is the formula to find the common ratio?
r=t_1-t_2
r=\frac{t_1}{t_2}
r=\frac{t_2}{t_1}
r=t_2-t_1
13
Identify the recursive formula to find the next term in an arithmetic sequence.
a_n=a_1+(n-1)d
a_n=a_{n-1}+d
a_n=a_1\cdot r^{n-1}
a_n=a_{_{n-1}}\cdot r
14
A sequence is recursively defined as f(1)=16 and f(n) = 1/2 f(n-1) for n≥2. What is f(2)?
8
2
4
6
15
In an arithmetic sequence A(1)=7 and the common difference is -1. What is the fifth term of the sequence?
2
3
7
-7
16
Bacteria grows geometrically and on day 3, there are 900 cells, day 7 there are 8,100 cells. How many cells on day 5?
1,750 cells
2,700 cells
1,800 cells
3,670 cells
17
Is the sequence: 4, 6, 8, ... arithmetic, geometric or neither? How do you know?
neither
arithmetic
geometric
both
