Arithmetic Sequences

LEARNING TARGET:

•Recognizing when a sequence of numbers forms
of an arithmetic sequence.

•Write terms of an arithmetic sequence

•Be able to determine the common difference in an
arithmetic sequence.

2

An arithmetic sequence is a
sequence of numbers in which the
difference between consecutive
terms is constant. This constant
difference is called the “common
difference.”

• Arithmetic sequences follow a pattern of adding a fixed

amount from one term to the next. The number being added
to each term is constant (always the same).
a1, (a1 + d), (a1 + 2d), (a1 + 3d), …

• The fixed amount is called the common

difference, d, referring to the fact that the difference
between two successive terms yields the constant value that
was added. To find the common difference, subtract the first
term from the second term.

•Arithmetic sequences have a linear nature when graphed as
a scatter plot. The domain consists of the counting numbers
1, 2, 3, 4, ... (representing the location) and the range
consists of the actual terms. In the graph shown, the x-axis
increases by a constant value of one, the y value increases
by a constant value of 3.

EXAMPLES

Arithmetic Sequences:

Common Difference, d:

1,6,11,16,21,26,...

D=5. A 5 is added to each term to
arrive at the next term. OR... the
difference a2 - a1 = 5

10,8,6,4,2,0,-2,-4,...

D=-2. A –2 is added to each term
to arrive at the next term OR... the
difference a2 - a1 = -2

1, ½, 0, -½,...

D=-½. A –½ is added to each term
to arrive at the next term OR... the
difference a2 - a1 = -1/2

5

EXIT TICKET

6

1) {-5, -1, 3, 7, …} ;a9

2) {20, 11, 2, -7, -16, ...} ;a10

3) {-6, -9, -12, -15, …} ; a11

4) {8, 9.5, 11,12.5, …} ; a12

QUESTIONS ?