UNIT 1 - ARITHMETIC & GEOMETRIC SEQUENCES
Task #1 – Catering Problem (Arithmetic Sequences)
Common Core: HS.F-BF.1a, 2
MA40: ALGEBRA 2
Name:
Period:
INVESTIGATION – Catering Problem: A square table seats 4 people.
Two square tables pushed together seat 6 people. Three tables pushed
together seat 8 people. How many people can sit at 10 tables pushed
together? How many tables are needed to seat 32 people?
1.
Describe the pattern that you see in the figures above. What do you
notice in the number of seats as you add more and more tables?
2.
Complete the table.
# of Tables
1
2
3
4
5
6
7
8
9
# of People
Table Scratch Work:
3.
Consider the pattern described in the table. Write an expression that
describes the number of seats that will be available by adding another
table to the previous arrangement of tables.
4.
Consider the table again. Write an expression that represents the
number of seats for any amount of tables.
Task #1 – Catering Problem (Arithmetic Sequences) – (continued)
DEVELOPING THE MATH CONCEPTS & TERMS
Sequence – A set of numbers in a specific order.
Find the next three terms of the sequence.
a) 1, 6, 11, 16, 21, ________, ________, ________
b) 2, 6, 18, 54, 162, ________, ________, ________
c)
5, -16, 27, -38, 49, ________, ________, ________
Recursive Formula – A recursive rule gives the beginning term(s) of a
sequence and then a recursive equation that tells how an is related to one
or more preceding terms.
Find the first four terms of the sequence defined by the recursive rule.
a)
a1  3, an  an1  5
b)
a0  3, a1  7, an  an1  an2
a1  ________
a0  ______, a1  ________
a2  _______________  ______
a2  _______________  ______
a3  _______________  ______
a3  _______________  ______
a4  _______________  ______
a4  _______________  ______
______,______,______,______,
________________________
sequence
sequence
Explicit Formula –An explicit rule gives an as a function of the term’s
position number n in the sequence.
Find the first four terms of the sequence defined by the explicit rule.
a)
an  n 2  2
b)
an  2  3n
a1  _______________  ______
a1  _______________  ______
a2  _______________  ______
a2  _______________  ______
a3  _______________  ______
a3  _______________  ______
a4  _______________  ______
a4  _______________  ______
______,______,______,______,
______,______,______,_____,
sequence
sequence
Task #1 – Catering Problem (Arithmetic Sequences) – (continued)
Arithmetic Sequence – A sequence where the difference between
consecutive terms is constant. The constant difference is called the
common difference and is denoted by d .
Decide whether the sequence is arithmetic. What is the common
difference?
a) 7, 1,  5, -11,  17, ...
c)
b)
3,  9,  27, -81, ...
1 1 3
5
, , , 1, , ...
4 2 4
4
Find the first four terms of the sequence defined by the arithmetic rule.
a)
a1  5, an  an1  2
b)
an  2.5n  3
a1  _______________  ______
a1  _______________  ______
a2  _______________  ______
a2  _______________  ______
a3  _______________  ______
a3  _______________  ______
a4  _______________  ______
a4  _______________  ______
______,______,______,______,
______,______,______,_____,
sequence
c)
sequence
What makes these two sequences arithmetic? Both rules are
arithmetic rules. How can this be when they are both so different?
Be specific.
TYING THINGS TOGETHER
Consider the Catering problem discussed earlier.
Summary:
5.
Does the table represent a sequence? Explain.
6.
Does the table represent an arithmetic sequence? Explain.
7.
Consider the answer in problem #3. Does this expression best fit the
definition of a Recursive Formula or an Explicit Formula. Explain. If
you haven’t already, rewrite the expression as an equation.
8.
Consider the answer in problem #4. Does this expression best fit the
definition of a Recursive Formula or an Explicit Formula. Explain. If
you haven’t already, rewrite the expression as an equation.