# Arithmetic Sequences Finding the nth Term ### 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