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Unit 2
Lesson 19
Arithmetic Sequences
Objectives
 I can decipher a pattern in a number sequence
 I can write explicit and recursive formulas of arithmetic sequences
Warm Up: write the next 3 terms of the sequence
1, 2, 2, 4, 8, 32…..
1, 1, 2, 3, 5, 8, 13, 21……
3, 5, 7, 9…..
25, 22, 19, 16……
A sequence is an arrangement of numbers or objects that follow
a rule or a pattern.
Each number in a sequence is called a term. The variable a is
often used to stand for the terms in a sequence. The first term
is 𝒂𝟏 , the second is 𝒂𝟐 , and so on. The nth term of the sequence
is written 𝒂𝒏 , where n can be any positive integer.
In an arithmetic sequence, each term is found by adding a fixed
number, called the common difference (d), to the previous term.
Are any of the warm ups examples of arithmetic sequences?
If so, what is d?
There are two ways to write sequence formulas—recursive and
explicit.
In the recursive process, finding a term depends on knowing a
previous term, so you MUST define at least one previous term.
The recursive definition looks like this
𝒂𝒏 = 𝒂𝒏−𝟏
+ d
Let’s Try….recursive equation
Let our sequence be
2, 4, 6, 8….
𝒂𝒏 = 𝒂𝒏−𝟏 + d
The explicit definition looks like this
𝒂𝒏 = 𝒂𝟏 + (n – 1)d
Let’s Try….explicit equation
28, 24, 20, 16….
Write the explicit equation for this arithmetic sequence
Write the recursive equation too!!
In a certain arithmetic sequence, each term is found by
subtracting 4.5 from the previous term. If the first term in the
sequence is 10, what is the 9th term in the sequence.
Write the explicit formula to find 𝑎𝑛
You try……….
5, 9, 13, 17, 21,…..
write the recursive equation
write the explicit formula
find the 15th term
10, 3, -4, -11, -18,…..
write the recursive equation
write the explicit formula
find the 18th term
Ami is training for a long distance race. She ran for 30 minutes per
day on three days this week. Each week she will increase her daily
running time by 5 minutes. By the 6th week, for how many minutes
will she run each day that she trains?
Name: _________________________
Unit 2 Lesson 19
Determine if the sequence is arithmetic. If it is, identify the
common difference.
1.
5, 3, 1, -1, -3, …..
2.
2, 2, 4, 6, 10, …..
3.
3/2, 5/2, 7/2, 9/2, 11/2,…
4.
3, 2.4, 1.8, 1.2,…..
Write a recursive and an explicit formula for each sequence.
5.
11, 15, 19, 23, …..
6.
100, 88, 76, 64,…..
𝑎𝑛 = _________________
𝑎𝑛 = _________________
𝑎𝑛 = _________________
𝑎𝑛 = _________________
7. 𝑎1 = 14
8.
d=6
𝑎1 = 0
d = 1/3
𝑎𝑛 = _________________
𝑎𝑛 = _________________
𝑎𝑛 = _________________
𝑎𝑛 = _________________
Find the indicated term in the arithmetic sequence.
9.
If
find 𝑎10
𝑎1 = 3 and 𝑎2 = 5
10.
If 𝑎1 = 3 and d = -3
find 𝑎4
11. Granny is knitting a 2 meters long scarf. On day 1 she finished
with 18 cm. On every following day she adds 4 cm to the scarf. How
many days will it take her to finish the scarf?