1. Recognizing and extending arithmetic sequences
Lesson 34
Recognizing and extending arithmetic sequences

2. sequences
A sequence of numbers can be formed using a variety of patterns and operations.
A sequence is a list of numbers that follow a rule, and each number in the sequence is called a term of the sequence.
An arithmetic sequence has a constant difference between 2 consecutive terms
1,3,5,7,… Arithmetic sequence
7,4,1,-2,… Arithmetic sequence
2,6,18,54,…
1,4,9,16

3. Arithmetic sequence
An arithmetic sequence has a constant difference between every 2 consecutive terms
To find the common difference, choose any term and subtract it from the previous term.
If the sequence does not have a common difference, then it is not arithmetic.

4. Recognizing arithmetic sequences
Determine if the following are arithmetic sequences and find the common difference if they are:
1) 7,12,17,22,…
2) 11,4,-3,-10,…
3) 4,8,16,32,64,…
4) 3,6,12,24,…

5. Arithmetic sequence formula
To find the next term in a sequence:
an = a n-1 + d
a1 = first term
d = common difference
n = term number
Find the first 4 terms of an arithmetic sequence if the first term is -2 and the common difference is 7
a2 = a
a2 = = 5
a3 = a
a3 = = 12

6. Finding the nth term in arithmetic sequences
an = a1 + (n-1)d
a1 = 1st term d = common difference
Find the 10th term of the sequence 3,11,19,27…
1st term = 3 common difference = 9
a10 = 3 + (10-1)8
= 3 + 9(8)= = 75

7. examples Find the 12th term of the sequence 3,10,17,…
3, 3 1/4, 3 1/2, 3 3/4,….
Find the 10th tern of the sequence
1/4, 3/4, 5/4, 7/4, …
Use the rule
an = -5 + (n-1)(-2) to find the 8th and 20th terms of the sequence