Do Now: Fill in the chart
ai+1 = ai + 4
4
a1
a2
4+ 4
a3
8+4
8
16
16 + 4
A little review:
sequence ­ an ordered set of
numbers. The elements of the
list are called the terms of the
sequence.
1
Sequences ­ an ordered list of elements
Term
Number
Sequence Term
Term
Term
1
4
a1
4
2
8
a2
8
3
12
a3
12
4
16
a4
16
5
20
a5
20
New Notation
an
f(1)
f(2)
f(3)
f(4)
f(5)
f(n)
{f(1), f(2), f(3), ... f(n)}
f(1) is the first term of the sequence
f(2) is the second term of the sequence
etc.
f(n)is the nth term of the sequence
2
Before we use our new notation in
sequences....
Do you see a pattern? Describe it in words.
1) 5, 6, 7, 8, 9, ...
2) 8, 10,12, 14, 16, ...
3) 4, 7, 10, 13, 16, ...
Arithmetic Sequences
Day 1
3
arithmetic sequence ­
a sequence in which the difference of any 2
consecutive terms is constant.
Common difference (d) ­ the difference
between the 2 consecutive terms
Finding the common difference (d)
Examples:
5, 6, 7, 8, 9, ...
d = ______
8, 10, 12, 14, 16,.. d = ______
4, 7, 10, 13, 16...
d = ______
4
Find the 8th term of each arithmetic
sequence:
5, 6, 7, 8, 9, ...
f(8)= ______
8, 10, 12, 14, 16,... f(8)= ______
4, 7, 10, 13, 16...
f(8)= ______
What if you were asked to find f(20), f(55),
or f(600)?
It is not realistic to complete that task
without a formula.
5
To find the nth term f(n):
f(n) = f(1) +(n-1)d
f(1) is the first term
d is the common difference
or f(n) = f(1) +d(n-1)
Write a formula for the sequence and find
the indicated term:
1) 5, 6, 7, 8, 9, ... f(n) = f(1) +d(n-1)
Find f(48)
6
2) 8, 10, 12, 14, 16,...
f(n) = f(1) +d(n-1)
Find f(67)
3) 4, 7, 10, 13, 16...
f(n) = f(1) +d(n-1)
Find f(52)
7
4) ­8, 12, 32, 52,...
f(n) = f(1) +d(n-1)
Find f(26)
5) 30, 25, 20, 15,...
f(n) = f(1) +d(n-1)
Find f(20)
8
6) 20, 17, 14, 11,...
f(n) = f(1) +d(n-1)
Find f(40)
7) 30, 28, 26, 24,...
f(n) = f(1) +d(n-1)
Find f(50)
9
If needed
More Practice­Find the formula and specific term:
8) 2, 5, 8, 11, 14 . . .
f(n) = f(1) +d(n-1)
9) 15, 11, 7, 3 . . .
f(n) = f(1) +d(n-1)
Find f(40)
Find f(10)
Class work:
Worksheet
10
Determine whether each sequence is arithmetic. If so, find the
common difference:
1) 28, 35, 42, 49, ...
2) 23, 8, -7, -22, ...
3) 9, 34, 59, 84, ...
4) 12, 24, 21, 38, ...
Find the First 4 terms and the stated term given the
arithetic sequence, with a1 as the 1st term
5) an = 114 - 100n, a16
7) an= 22 - 9n, a17
6) an= 22 - 3n, a10
8) an= -18 + 23n, a6
11
Given the first term and common difference, find the
first four terms and the formulas
9) a1= 11, d = 50
11) a1= 6, d = 4
10) a1= 26, d = -20
12) a1= 25, d = 10
Homework
12
13
14