# Arithmetic Sequences Finding the nth Term ### 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

.

### Finding the nth Term

• 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

### Practice Problems

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