The document discusses arithmetic sequences, which are patterns of numbers where each term is found by adding a constant value to the previous term. It provides examples of arithmetic sequences with different common differences and shows how to write equations to determine the nth term. It also explains how to find terms within an arithmetic sequence and determine arithmetic means between two non-consecutive terms.

1. What comes next?
An arithmetic
3, 5, 7, 9, 11 13 15
__, __, __ sequence is a
pattern of
+2 +2 +2 +2 +2 +2
numbers in
Common difference which each
d=2 number is
a1 = 3 found by adding
a constant to
a2 = 5 the number
before it.
a3 = 7

2. What’s the common difference?
8, 10.5, 13, 15.5, …
d = 2.5
9, 5, 1, -3, …
d = -4

3. 3, 5, 7, 9, 11, 13, 15, …
+2 +2 +2
a1 = 3
a2 = 5 3 + 1(2)
a3 = 7 3 + 2(2)
a4 = 9 3 + 3(2)
an = a1 + (n – 1)d

4. Write an equation for the nth term of the
arithmetic sequence –8, –6, –4, ….
Find the 80th term of the sequence
a80 = 2(80) – 10
= 160 – 10
= 150

5. Complete the statement for the arithmetic sequence:
124 is the ____ term of -2, 5, 12, …
124 -2 7
124 = -2 + 7n – 7
124 = 7n – 9
133 = 7n
19 = n

6. The terms between any two nonconsecutive
terms of an arithmetic sequence are arithmetic
means.
Find the three arithmetic means between 21 and 45.
27 33 39
21, ___, ___, ___, 45, ...,
+d +d +d +d