Download Arithmetic Sequences - hrsbstaff.ednet.ns.ca

ARITHMETIC
SEQUENCES
Feb 4th 2015
Staircase Numbers
A staircase number is created when
you add the number of blocks in
any two consecutive columns. The
first staircase number is 3, the
second is 5, and the third is 7
1
7
2
3
4
5
6
Let’s put our staircase numbers in a table
1
2
3
4
Staircase 3
Number
5
7
9 11 13 15 17 19 21
Term
5
6
7
8
9
1
7
10
2
3
4
5
6
Arithmetic Sequences
Sequence-An ordered list of elements arranged in an order so that it
follows a pattern or a rule
Arithmetic Sequence – a sequence in which the difference between
consecutive terms is consistent, in other words, the same value is
added to each term to create the next term.
Terms
(position)
Sequence
(value)
a
b
c
d
e
Term-each item in a sequence.
t1 = the first term
t2 = the second term
tn = the nth term
Terms
(position)
Sequence
(value)
a
b
c
d
e
Example 1
For example, for the sequence {3, 6, 9, 12, 15}
t1 =
t4 =
A finite sequence is a sequence that eventually
terminates.
An infinite sequence is a sequence that continues
indefinitely.
We can make new sequences from already existing
sequences “sequences of differences”.
Find the difference between successive terms:
{t1, t2, t3, t4, t5, t6}
S.O.D. = {t2-t1, t3-t2, t4-t3, t5-t4,t6-t5}
Example 2
S.O.D. = {t2-t1, t3-t2, t4-t3, t6-t5}
Find the sequence of differences for:
(a) {3, 7, 11, 15, 19, 23}
(b) {0.5, 2, 3.5, 5, 6.5}
If the items in the sequence of difference are
the same then this number is called a
common difference.
Equation
Consider this sequence,
Terms
Sequence
101
133
165
197
Can we create an equation between the term
position and value?
Terms
Sequence
101
133
165
197
Sequence of
difference
133-101=32
165-133=32
197-165=32
S.O.D={32,32,32}
101
101+(32)
10+(32)+(32)
10+(32)+(32)+(32)
t1
t1+d
t1+d+d
=t1+2d
t1+d+d+d
=t1+3d
expressed using
first term and
common difference
Sequence
General
Sequence
General Term
•
b) How many terms in each of the following
s sequences?
{9,4,-1,…,-146}
HOMEWORK
pg 16 #1-6, 8, 11, 12, 20