Arithmetic Sequence A sequence of terms that have

Arithmetic Sequence A sequence of terms that have a common difference between them

Geometric Sequence A sequence of terms that have a common ratio between them

Explicit Formula used to find the th n term of a sequence

Explicit Formula for Arithmetic Sequence an is the value of the term you want to find a 1 is the first term n is the term you want to find d is the common difference

Explicit Formula for Geometric Sequence an is the value of the term you want to find a 1 is the first term n is the term you want to find r is the common ratio

How to find if arithmetic or geometric Step 1: Subtract the 1 st term from the 2 nd term Step 2: Subtract the 2 nd term from the 3 rd term Step 3: If the results are the same, it is an arithmetic sequence, and the result is the common difference, d. Step 4: If not arithmetic, divide the 2 nd term by the 1 st term. Step 5: Divide the 3 rd term by the 2 nd term. Step 6: If the results are the same, it is a geometric sequence, and the result is the common ratio, r.

Arithmetic or Geometric? Example: -22, -15, -8, -1, … Arithmetic d=7

Arithmetic or Geometric? Example: 7, 4, 1, -2, -5 Arithmetic d = -3

Arithmetic or Geometric? Example: 256, 64, 16, 4, … Geometric r = 1/4

Arithmetic or Geometric? Example: Geometric r = 2/3

Find the common difference, the explicit formula, and the tenth term. 3, 9, 15, 21, … d=6 an = 6 n – 3 a 10 = 57

Find the common ratio, the explicit formula, and the seventh term. 3, 1. 5, 0. 75, 0. 375, …

The fifth term is 1, 792. The constant ratio is 4. Write the explicit formula.

Homework Sequence Practice WS 1 -14