Algebra
Lesson 4-7
Arithmetic Sequences
Vocabulary-
Sequence: a set of numbers in a specific order
Terms: the numbers in the sequence
Arithmetic Sequence: a sequence that has a pattern between numbers
Common Difference: the pattern of the sequence
Examples:
1. Identify Arithmetic Sequences
-Determine whether each sequence is arithmetic, and tell why.
a. 1, 4, 8, 12, ...
1 à 4 à 8 à 12
+4 +4 +4
This is an arithmetic sequence because it has a pattern between the numbers.
1, 8, 5, 4, ...
1 à 8 à 5 à 4
+7 -3 -1
This is not an arithmetic sequence because there is no pattern between the numbers.
5, 6, 8, 11, 15, 20, 26, ...
+1 +2 +3 +4 +5 +6
This is not an arithmetic sequence because the difference between terms is not constant.
2.Extend a Sequence
Find the next three terms of the sequence.
50, 43, 36, 29, ...
50 à 43 à 36 à 29
-7 -7 -7
29 à 22 à 15 à 8
-7 -7 -7
The next three terms are 22, 15, and 8
100, 150, 200, 250, 300, 350, ...
+50 +50 +50 +50 +50
The next three terms are 400, 450, and 500.
3. Using the following data, tell whether the Weather Balloon's altitude in relation to the time is an arithmetic sequence. (To see what a weather ballon looks like, look below at the pictures)
Time (s): 1 2 3 4 5 6
Altitude (ft):5.8 6.8 7.8 8.8 9.8 10.8
-For each second, the balloon rises 1 foot. Since there is a common difference (of 1 foot), it IS an arithmetic sequence.
Additional Information:
Key Concept: nth Term of an Arithmetic Sequence
The nth term 'an' (a sub-n) of an arithmetic sequence with first term a1 (a sub-1) and common difference d is given by:
an = a1 + (n-1)d
where n is a positive integer. *HINT: you will use the formula above (highlighted) a lot. Know it!
4. Find the nth term in each arithmetic sequence.
a1=5, d=5, n=25
5+(25-1)5
5+24(5)
5+120
125
5.Write an equation for the nth term of each arithmetic sequence.
-3, -6, -9, -12, ...
an=-3+(n-1)-3
an=-3-3n+3
an=-3n
Online resources
Pictures:
Okay, so you want to find out how many seats are in the front row of a theater (I don't really know why...Maybe you are designing a theater?), but you don't want to count them all out. If you know by how many seats they
decrease as you get closer to the stage, how many seats are in the back row, and what number row the
front row is, you can figure it out! Just use your knowledge on Arithmetic Sequences!
You can also use your knowledge on Arithmetic Sequences to figure out the location/ altitude of a weather balloon. (There are some examples in our book that demonstrate this, also.)This page by: JG CAO