3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
3.8 EXPLICIT FORMULAS FOR SEQUENCES
TERMINOLOGY‐
Recall: a SEQUENCE is A
SET OF NUMBERS IN A LIST.
Recall: THE NOTATION t2=9 means “9 IS THE SECOND TERM OF THE SEQUENCE”
The SUBSCRIPT= THE
SMALL #BELOW THE VARIABLE, TELLS
THE TERM OF THE SEQUENCE
t means the nth term in the sequence.
A General Term.
The subscript n= n
3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
EXPLICIT FORMULA‐
To find a term in a sequence,
the subscript #
substitute _________________
n
value
in for _______ to find each ________.
A: FIND THE FIRST FOUR TERMS OF THE SEQUENCE
t1=2(__)+5=
t2=2(__)+5=
t3=2(__)+5=
t4=2(__)+5=
3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
C: A GROUP OF STUDENTS TOOK A BIKE TRIP ACROSS THE COUNTRY, AVERAGING
60 MILES OF RIDING EACH DAY. THE SEQUENCE
GIVES THE DISTANCE
THEY HAVE BIKED AFTER N DAYS. HOW FAR HAS THE GROUP BIKED AFTER 7 DAYS?
RECALL: AN ARITHMETIC SEQUENCE IS when there's a constant term being added or subtracted
3.8 Explicit Formulas and Sequences.notebook
the first term
constant difference
FIND THE RECURSIVE FORMULA FOR THE SEQUENCE.
October 06, 2011
3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
To the extreme,
I rock a mic like a... FIND THE RECURSIVE FORMULA FOR THE SEQUENCE.
= 50 AND
F: TWO TERMS OF AN ARITHMETIC SEQUENCE ARE GIVEN
WRITE AN EXPLICIT FORMULA FOR THE SEQUENCE FOLLOWING THE STEPS BELOW:
A.) FIND D (DISTANCE)
B.) USE TERM
TO FIND THE FIRST TERM
C.) WRITE EXPLICIT FORMULA FOR THE SEQUENCE.
.
= 25.
3.8 Explicit Formulas and Sequences.notebook
October 06, 2011
G: IN A CONCERT HALL THE FIRST ROW HAS 20 SEATS IN IT,
AND EACH SUBSEQUENT ROW HAS TWO MORE SEATS THAN
THE ROW IN FRONT OF IT. IF THE LAST ROW HAS 64 SEATS,
HOW MANY ROWS ARE IN THE CONCERT HALL?
FIND THE FIRST FOUR TERMS OF THE SEQUENCE.
1.
FIND THE 32ND TERM.
t32 = 4,104
.
3.8 Explicit Formulas and Sequences.notebook
1.
October 06, 2011
WRITE THE EXPLICIT FORMULA FOR THE ARITHMETIC SEQUENCE:
FIND THE 100TH TERM.
a100 = ‐132.5
3. A TV SHOPPING CLUB THAT HAD 1218 GOLD NECKLACES, EACH WORTH $125,
SOLD 42 NECKLACES EACH MINUTE THE ITEM WAS FEATURED.
a. WRITE AN EXPLICIT FORMULA THAT GIVES THE NUMBER OF
NECKLACES LEFT AFTER N MINUTES.
b. HOW MANY MINUTES DOES THIS ITEM NEED TO BE FEATURED
BEFORE THE CLUB WOULD SELL OUT?
3.8 Explicit Formulas and Sequences.notebook
4. IS THE SEQUENCE
October 06, 2011
ARITHMETIC OR NOT? WHY?