Arithmetic Sequences

In an arithmetic sequence, the difference between consecutive terms is constant.

The difference is called the common difference.

To find d: 2nd term – 1st term

Arithmetic?

1. 2, 4, 8, 16

2. 6, 12, 18

3. 48, 45, 42

4. 2, 5, 7, 12

Arithmetic Sequence Formulas Recursive Formula an = an-1 + d

Explicit Formula an = a1 + (n-1)d

an = nth term a1 = 1st term n = number of terms

d = common difference

Examples

Find the 20th term of each sequence

1. 213, 201, 189, 177…

2. .0023, .0025, .0027…

More examples

Find the 17th term of the sequence:

3. a16 = 18, d = 5

Find the missing term

Use arithmetic mean = average!

4. 84, _______, 110

5. 24, _______, 57