1. Pre Calculus 11 Section 1.1 Arithmetic Sequences

2. i) Arithmetic Sequences:
A sequence is an ordered list of objects or numbers
An “arithmetic sequence” is a list of numbers where each term increases or decreases by a common difference (d) [same value]
Ex: Find the Common Difference:
i) 3, 6, 9, 12,….
ii) – 5, – 11, – 17, ….
iii) 19, 11, 4, -2,….
The difference between the terms are not consistent
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3. Patterns in Arithmetic sequences are seen in everything ie: wage increase, costs vs time, cost vs quantity
Jason works at the PNE selling water. For every bottle water he sells, he earns 35cents as commission. Suppose he earns $64 a day plus commission, how much will he earn if he sold 200 bottles? How many bottles will he need to sell to earn $300?
For every 3 minutes in a taxi ride, the cost increases by $ If the initial cost is $5, how much will it cost for 9min? 12min? And 15min? Or if you have only $25, how long can you afford?
In this section, you will learn to find the value of each term in an arithmetic sequence, how many terms there are, common difference, and how to apply it in real applications
Suppose Jason works at the PNE and he earns commission on his sales. If he sold 200 bottles, he earns $134. If he sold 300 bottles he earns $169. How much commission does he earn from each bottle?
After sitting in a taxi for 9 minutes, Sally realizes the cost of the ride was $ Three minutes later the cost was $ How much will the ride be in 30minutes?

4. Working with Arithmetic Sequences
Ex: In each of the sequences below, indicate whether if it is an arithmetic sequence. If yes, find the common difference and the value of the 10th term
i) 13, 21, 29,....
ii) -6, -10, -14,....
iii) 4, 10, 17, …..
Yes it is a A.S. because each term is increasing by 8 (common difference)
Yes it is a A.S. because each term is decreasing by 4 (common difference: – 4 )
No it is not a A.S. because difference is not consistent!
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5. How does an arithmetic sequence work?
The first term of an A.S. is called “a” or “t1”
Each term after the first adds another common difference “d”
The value of each term is denoted “tn”, where “n” is the order of the term
The number of common differences “d” in each term is one less than it “n” value
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6. Ex: Given the sequence: 6, 11, 16… find the 32nd term.
Write down the formula:
Identify parts you know:
Substitute the values into formula and calculate:
tn = a + (n – 1)d
= 6 + (32 – 1)(5)
= 6 + (31)(5) =
= 161
The 32nd term is 161

7. Practice: Solve each of the problems below
Find the 30th term in the sequence:
Find the 200th term in the sequence:
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8. Write down the formula: tn = a + (n – 1)d Identify parts you know:
Ex: An arithmetic sequence is 53, 49, 45, One term in this sequence is Which term is it?
Write down the formula: tn = a + (n – 1)d
Identify parts you know:
n = ?, a = 53, d = 49 – 53 = -4, tn = -107
Sub parts into formula and calculate:
tn = a + (n – 1)d
– 107 = 53 + (n – 1)(– 4)
– 107 = 53 – 4n + 4
– 107 = 57 – 4n
– 164 = – 4n
41 = n
Notice the –ve sign. Why? Because of the
Distributive property

9. Practice: Solve each of the problems below
What term is -523 in the arithmetic sequence?
–523 is the 65th term!
Find the 3 missing terms in the arithmetic sequence:
Therefore, the numbers will be:
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10. _, ___, __, __, 7, ___, ___, ___, ___, ___, ___, -49
Ex: In an arithmetic sequence, the 5th term is 7 and the 12th term is -49
List the sequence and show the first 5 terms.
Write the general term for the sequence.
How many terms are greater than -100?
List the sequence first
_, ___, __, __, 7, ___, ___, ___, ___, ___, ___, -49
Find the common difference
To find previous terms, just subtract the common difference.
Work backwards!!

11. Write down the formula: tn = a + (n – 1)d
List parts you know: a = 39, d = -8
Sub parts into formula:
tn = 39 + (n – 1)(-8)
= 39 – 8n + 8 Dist. Prop causes the sign change
= -8n This is the general term
Do a check by finding t5
t5 = -8n + 47
= -8(5) + 47 =
= 7

12. To find terms greater than -100, you need some kind of inequality.
Set up the inequality, then solve for “n”
-8n + 47 > -100
-8n > -100 – 47
-8n > -147
n < -147 -8
n <
Notice the inequality “switched” when
divided by a –ve number
Since will give you exactly -100, only 18 terms is allowed because the # of terms must be smaller than (besides, you can’t have “.375” of a term)

13. HW: Assignment 1.1 Arithmetic sequences
Optional assignment p16 #1-6 odd letters, 8, 10, 11, 13, 17, 18