Coordinate Algebra Arithmetic and Geometric Sequences Learning Target

Coordinate Algebra Arithmetic and Geometric Sequences Learning Target: Students can use the explicit formula to find the nth term of a sequence.

Arithmetic Sequences Geometric Sequences (Common difference) (common ratio) Explicit Formula Recursiv e Formula

• A sequence is a list of numbers that may form a pattern. • Each number in a sequence is called a term. Example: The distance between you and a lightning strike can be approximated by using a sequence. Times (s) Distance (mi) Each distance is 0. 2 miles greater than the previous distance. 1 0. 2 *When the terms of a sequence differ by the same nonzero number d, the sequence is an arithmetic sequence and d is the common difference. 2 0. 4 3 0. 6 4 0. 8 5 1. 0 6 1. 2 7 1. 4 8 1. 6

Arithmetic Sequence A sequence of terms that have a common difference (d) between them -Subtract terms right to left

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. • 12, 8, 4, 0, … Step 1: Find the difference between successive terms. Add -4 to each term to find the next term. The sequence is arithmetic and the common difference is -4. • Step 2: Use the common difference to find the next 3 terms. 0 -4 = -4, -4 – 4 = -8, -8 – 4 = -12

• 1, 4, 9, 16, … • Step 1: Find the difference between successive terms. 1 + 3 = 4, 4 + 5 = 9, 9 + 7 = 16 • The difference between successive terms is not the same, so the sequence is not arithmetic.

Explicit Formula for Arithmetic Sequence (Finding the nth term)

Explicit Formula for Arithmetic Sequences a 1 + (n-1)d = an (Allows us to find ANY term in a sequence) a 1= 1 st term n= the number of the term you are looking for d= common difference an= the value of the term that you are looking for

Geometric Sequence A sequence of terms that have a common ratio (r) between them -Divide terms right to left

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

Explicit Formula for Geometric Sequence

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, … a 10 = 57 d=6

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