Page 39 - Math Course 1 (Book 1)

Arithmetic Sequences

Mo. 1

Lesson 7 Common difference
The difference between the terms of a sequence is
called the common difference.

20, 30, 40, 50, 60,

KEY CONCEPTS: ( +10 is the common
1. Recognizing Arithmetic Sequence. +10 +10 +10 +10 difference )
2. Extend and write formulas for
arithmetic sequences.

Key Concept
MO. 1 - L7a

Recognizing Arithmetic Arithmetic Sequence
Sequence

An arithmetic sequence is a numerical pattern
that increases or decreases at a constant rate
Vocabulary A-Z or value called the common difference.

Let us learn some vocabulary

Writing Arithmetic Sequences

Sequence Words Each term of an arithmetic sequence
after the f rst term can be found by
is an ordered list of numbers.
adding the common difference to the
3 7 11 15 19 23 preceding term.

Symbols An arithmetic sequence can be found
as follows
a1, a1 + d1, a2 + d1, a3 + d...,

where d is the common difference,
a1 is the f rst term, a2 is the second
term, and so on.

nth Term of an Arithmetic
Sequence
Words The nth term an of an arithmetic
Term sequence with f rst term a1 and
Each number is called a term of the sequence. common difference d is given by

20, 30, 40, 50, 60,... 20,30,40,50,60 a = a1 + ( n - 1) d
Each number is n
+10 +10 +10 +10 called a term of where n is a positive integer.
the sequence.

Arithmetic sequence
is a sequence in which the difference between any
two consecutive terms is the same
20, 30, 40, 50, 60,

+10 +10 +10 +10
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