Arithmetic Sequences
•
• A pattern where all numbers are related by the same common difference.
• The common difference must be an addition or subtraction constant.
• The common difference can be used to predict future numbers in the pattern.
Ex. 4, 7, 10, 13, ___, ___, ___
The common difference in this pattern is +3 . Based on this information, you can say that the next 3 terms will be 16, 19, and 22 .
Ex. -1, -5, -9, ___, ___, ___
The common difference in this pattern is -4 . Based on this information, you can say that the next 3 terms will be -13, -17, and -21 .

• If you want to find a term in an arithmetic sequence that is far into the pattern, there is a formula to use.
a n
= a
1
+ (n – 1)(d) a n
= the answer term you are looking for in the sequence a
1
= the first term in the sequence n = the ordinal number term you are looking for in the sequence d = the common difference
Ex. 23, 18, 13, 8, … find the 63 rd term a n
= 23 + (63
– 1)(-5) a n
= 23 + 62(-5) a n
= 23 + (-310) = -287

1.
11, 13, 15, 17, … Find the 85 th term
2.
25, 22, 19, 16, … Find the 50 th term
3. a
1
= -15 d = +4 Find the 71 st term
4. a n
= 255 d = +3 a
1
= 36 Find n