Transcript Sequences Day 2 Recursive Arithmetic Formula

Week 4
Warm Up
1) Geometric or Arithmetic?
-2, 4, -8, 16, -32, 64,…
09.07.11
Homework
Geometry
Sequences
Day 2
Term
I will identify term numbers and
terms of sequences.
The value of the number in the sequence.
Terms
Ex 1
3,
7,
11,
15,
19
1st
2nd
3rd
4th
5th
Term #’s
Term #
The order in the sequence.
Geometry
Sequences
Day 2
Term
I will identify term numbers and
terms of sequences.
The value of the number in the sequence.
Terms
Ex 1
3,
7,
11,
15,
19
1st
2nd
3rd
4th
5th
Term #’s
Term #
The order in the sequence.
3, 7, 11, 15, 19, . . .
Term #
t1 is read “t sub 1.”
t1 = 3
means the first term is 3
t2 = 7
the second term is 7
t3 = 11
the third term is 11
Ex 2
tn
-6, -1, 4, 9, 14, . . .
represents the nth term in the sequence
is read “t sub n.”
if n = 1 then tn = -6
if n = 3 then
tn = 4
if n = 6 then tn = 19
Ex 3
tn-1
-8, 1, 10, 19, 28, . . .
represents the previous term to the nth term
if n = 2 then tn-1 = -8
tn-2
represents two previous terms to the nth term
if n = 5 then tn-2 = 10
Ex 4
tn+1
-6, -1, 4, 9, 14, . . .
represents the next term after the nth term
if n = 2 then tn+1 = 4
if n = 4 then tn+2 =19
Ex 5
an
2,
9, 16, 23, 30, . . .
is read “a sub n.”
it’s the same as t1
if n = 4
then an+2
=
37
Ex 6
-4, 12, -36, 108, -324, . . .
if n = 6 then
an-1 = -324
if n = 6 then
an- 2 = 108
Arithmetic or Geometric
Starting with -4, multiply the previous
number by -3 to get the next number.
Fibonacci
Sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, . . .
Rule?
Starting with one, the sum of the two
previous terms equals the next term.
Review
Do: 1
What is a recursive formula?
-6, 12, -24, 48, -96, . . .
if n = 8
then
an-3 =
Rule?
Assignment:
Handout – Sequences CW 1.2
Recursive Formulas