Name______________________
Algebra 1
Period _____________
Date___________
Unit 3: Arithmetic and Geometric Sequences Review
1) Find a recursive formula for the sequence: 4, 6, 9, 13.5, …
2) Find a recursive formula for the sequence: 86, 43, 21.5, …
3) The common _____________ in the arithmetic sequence 3, -1, -5, -9, … is _____________
4) The common _____________ in the geometric sequence 3, 12, 48, … is _____________
5) Find the given term of each arithmetic sequence.
a)
5, 10, 15, 20,… the 17th term
b)
-2,-5,-8,-11,… The 41st term
6) Greg decides to run every day to prepare for lacrosse. He runs 2 miles the first day and then increases by
half a mile each day after that.
a) Is this arithmetic or geometric?
b) Write the explicit formula for the number of miles Greg will run on day n.
c) Determine how many miles Greg will run on day 6.
d) How many days will it take Greg to run 5.5 miles?
7) Use the geometric sequence in which a1= -5 and the recursive formula is 𝑎𝑛 =3(𝑎𝑛−1 ) to answer the
following questions:
a) What is the 5th term of the sequence?
b) What is the explicit formula?
8) Use the arithmetic sequence in which a1= 15 and the recursive formula is 𝑎𝑛 =(𝑎𝑛−1 ) + 9 to answer the
following questions:
a) What is the 3rd term of the sequence?
b) What is the explicit formula?
9) Determine whether each is arithmetic, geometric or neither. Where possible, write the explicit formula
a) 2 ,8, 14,20,…
_________________________
b) 1, 1, 2, 3,…
_________________________
c) 2.1, 1.4, 0.7, 0,…
__________________________
d) 2, 3, 4.5, 6.75, …
__________________________
e) 0.1, 0.3, 0.9, 2.7,…
_________________________
f)
_________________________
2, 10, 50, 250, …
g) 6, 18, 24, 38, …
_________________________
h) 9, 3, -1, -5, …
_________________________
10) Find the missing term(s) in each geometric sequence.
a)
20, 40,___,___,…
b)
___,6, 18,____,…
c)
-3,____,-12, 24,___,…
11) Write the formula for each of the sequences described below.
a) An arithmetic sequence with a1=3 and a common difference of 5.
Explicit:_______________________
Recursive:_____________________
b)A geometric Sequence with a1 = 4 and a common ratio of 3.
Explicit:_______________________
Recursive:_____________________
12) If school is cancelled the school secretary calls 2 teachers. Each of those teachers calls another 2
teachers. In the third round of call each of the 4 teachers calls another 2 teachers. If this pattern
continues how many teachers are called in the seventh round of calling.
13) A teacher is repeatedly enlarging a diagram on a photocopier. The function f(x) = 3(1.25)x
represents the length of the diagram, in centimeters, after x enlargements. What is the length after 5
enlargements? Round to the nearest centimeter.
14) Mandy’s new job has a starting salary of $16,000 and an annual increase of $800. How much will
she earn during her fifth year?
Name____KEY__________________
Algebra 1
Period _____________
Date___________
Unit 3: Arithmetic and Geometric Sequences Review
1) Find a recursive formula for the sequence: 4, 6, 9, 13.5, …
an = 1.5an-1
2) Find a recursive formula for the sequence: 86, 43, 21.5, …
𝟏
an = 𝟐an-1
3) The common ___difference_____ in the arithmetic sequence 3, -1, -5, -9, … is _____-4______
4) The common ___ratio/factor____ in the geometric sequence 3, 12, 48, … is _____4________
5) Find the given term of each arithmetic sequence.
a)
5, 10, 15, 20,… the 17th term
a17 = 85
b)
-2,-5,-8,-11,… The 41st term
a41 = -122
6) Greg decides to run every day to prepare for lacrosse. He runs 2 miles the first day and then increases by
half a mile each day after that.
a) Is this arithmetic or geometric?
arithmetic
b) Write the explicit formula for the number of miles Greg will run on day n.
an = 0.5n + 1.5
c) Determine how many miles Greg will run on day 6.
a6 = 4.5 miles
d) How many days will it take Greg to run 5.5 miles?
8 days
7) Use the geometric sequence in which a1= -5 and the recursive formula is 𝑎𝑛 =3(𝑎𝑛−1 ) to answer the
following questions:
a) What is the 5th term of the sequence?
a5= - 405
b) What is the explicit formula?
an = -5(3) n-1
8) Use the arithmetic sequence in which a1= 15 and the recursive formula is 𝑎𝑛 =(𝑎𝑛−1 ) + 9 to answer the
following questions:
a) What is the 3rd term of the sequence?
a3 = 33
b) What is the explicit formula?
an = 9n + 6
9) Determine whether each is arithmetic, geometric or neither. Where possible, write the explicit formula
a) 2, 8, 14, 20,…
____ an = 6n - 4___________
b) 1, 1, 2, 3,…
____neither______________
c) 2.1, 1.4, 0.7, 0,…
_____an = -0.7n + 2.8_______
d) 2, 3, 4.5, 6.75, …
_____an = 2(1.5) n-1_________
e) 0.1, 0.3, 0.9, 2.7,…
_____an = 0.1(3) n-1_________
f) 2, 10, 50, 250, …
_____an = 2(5)n-1___________
g) 6, 18, 24, 38, …
_____neither______________
h) 9, 3, -1, -5, …
_____neither______________
10) Find the missing term(s) in each geometric sequence.
a)
20, 40, _80__, _160_,…
b)
_2_, 6, 18, _54_,…
c)
-3, _6_,-12, 24, _-48_,…
11) Write the formula for each of the sequences described below.
a) An arithmetic sequence with a1=3 and a common difference of 5.
Explicit: _____an = 5n – 2 __________
Recursive: ___an = an-1 + 5 _________
b) A geometric Sequence with a1 = 4 and a common ratio of 3.
Explicit: ___an = 4(3) n-1________
Recursive: ___an = 3an-1 _______
12) If school is cancelled the school secretary calls 2 teachers. Each of those teachers calls another 2
teachers. In the third round of call each of the 4 teachers calls another 2 teachers. If this pattern
continues how many teachers are called in the seventh round of calling.
128 teachers
13) A teacher is repeatedly enlarging a diagram on a photocopier. The function f(x) = 3(1.25)x
represents the length of the diagram, in centimeters, after x enlargements. What is the length after 5
enlargements? Round to the nearest centimeter.
f(5) = 9 centimeters
14) Mandy’s new job has a starting salary of $16,000 and an annual increase of $800. How much will
she earn during her fifth year?
$19,200