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Chelsea

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Pre-Calculus

Arithmetic Sequences 

Arithmetic series

Pre_Calculus Unit 5.2 Notes
Topic: Arithmetic Sequences
Essential Question: How can I find the nth term of an arithmetic sequence?
Key Words
Summary
When
The difference between successive terms of a sequence is always
the same number, the sequence is called arithmetic.
Arithmetic
Sequence
- State the common difference for each arithmetic sequence.
a) 1, 5,9,13,....
b) 7,2, -3, -8,...
VVV
-5-5-5
- Determine if the following sequences are arithmetic sequence:
a) 4, 6, 8, 10, ...
VYV
b) 1, 3, 7, 11, ...
VVV
2 Ч Ч
222
yes
NO
For an arithmetic sequence:
=
c) a = 26, a₁2-38
12 = a₁ + (12-1)d=
a1-a
•%/₁+11d=38
8
= a₁ +18 -1)d=ta₁ 77d=26
nth term
Nth term of an arithmetic sequence: an-a1 +(n-1) d
Example - Find the formula for the n'" term of each of the following arithmetic
sequences, then apply it for the specific term.
a) a₁ = 3, d=2, a5 =?
n = a₁ + (^_^)α = 3+ (n-1)2
= 3+2n-2
2n+1
98=26= a₁ + 18-1)3=9₁+21
-> a₁ = 26-21:53
an=5+(n-131
a2= a₁ +d
a3 a2 +d = a₁ +d +d=a₁ +2 d
a4-a3 +d = a1 +2 d +d= a₁ +3 d
1st term
2:
4d=12-7d=3!
c) 2,4,8,16,...
VVV.
243
NO
subtrost
term number
common difference
b) a 12, d=7, a10=?
a₂ = 9,₁ +7=> 12=9₁ + 7 -> 9₁ = 5
an=5+7(n-1) = 5+7h-7=7n=2
a10 = 7(9)_2=61
d) a₁ =15, 9₁=18
913= x₁ +12d=18
- ( 9₂ = ₁ + 6α = 15)
6d=3-> d=1
9₁ +6142₂) 15-ja₁-12] Pre_Calculus Unit 5.2 Notes
Find the 41st term of the arithmetic sequence: 2,6,10,14,18,...
9=2
d=4
1=2 +4(n-1)
>
Topic: Arithmetic Sequences
)
941
Find the formula of the nth term of the sequence: 2,5,8,11,...
9₁=2
id=3
, an=2+3(n-1)
2 +4 (41-1) = 162
)
Edwin is getting better at math. On his first quiz he scored 57 points, then he scores
61 and 65 on his next two quizzes. If his scores continued to increase at the same
rate, what will be his score on his 9th quiz? Show all work.
57,61652.
a. Write an explicit formula for the sequence. Explain where you found the numbers
you are putting in the formula.
a₁ =57
d=61-57=4
an=a₁ + (n-1)d = 57 +(^-1) 4 = 4n+53
b. Identify the value of 9th term and explain where you found it. Use the explicit
formula to solve the problem.
aa=419)+53 = 89
c. Write your final answer as a sentence.
Edwin will get a grade of 89 in his 9th quiz

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Arithmetic Sequences

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying