Warm up f(x) = 3x + 5, g(x) = x – 15, k(x) = -9 Find 2f(x) + g(x). Find g(x) – f(x) – k(x).

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 Formula used to find the nth term of a sequence

Explicit Formula for Arithmetic 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, … d = 6 an = 6n – 3 a10 = 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 The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.

Arithmetic & Geometric Sequences Recursive

Recursive Formula a formula used to find the next term of a sequence when the previous term is known

Recursive Formula for Arithmetic Sequence

The first term is 1 for an = an-1 – 2. Find the next term. iRespond Question Fill-In F E0F52DA5-7735-0245-BFAF-D16246ED6B41 A.) -1;; B.) C.) D.) E.)

The first term is 1 for an = an-1 – 2. Find the third term. iRespond Question Fill-In F 403B2080-1CC6-0446-8168-67DE1A223E4E A.) -3;; B.) C.) D.) E.)

Ex: The first term is 1 for an = an-1 – 2. Find the next two terms.

Recursive Formula for Geometric Sequence

The first term is 320 for an = an-1 Find the next term. A.) -80;; B.) iRespond Question Fill-In F 2E6C59BB-017B-C344-BC20-96A452BFAE4A A.) -80;; B.) C.) D.) E.)

The first term is 320 for an = an-1 Find the third term. A.) 20;; B.) iRespond Question Fill-In F 4310E593-BA89-AC4D-BEBD-947CA710FD87 A.) 20;; B.) C.) D.) E.)

Ex: The first term is 320 for an = -1/4 an-1. Find the next two terms.

Find the next term x y 1 3 2 13 23 4 33 n A.) 43;; B.) C.) D.) E.) F iRespond Question F Fill-In 1D87A3AE-F65A-CA4C-A922-808473977155 x y 1 3 2 13 23 4 33 n A.) 43;; B.) C.) D.) E.)

Find the next term and write the recursive rule. y 1 3 2 13 23 4 33 n

Find the next term x y 1 16 2 40 3 100 4 250 n A.) 625;; B.) C.) D.) iRespond Question F Fill-In 9616F841-645E-6248-96FA-39F289FD5ABB x y 1 16 2 40 3 100 4 250 n A.) 625;; B.) C.) D.) E.)

Find the next term and write the recursive rule. y 1 16 2 40 3 100 4 250 n

Find the next term x y 1 2 14 3 98 4 686 n A.) 4802;; B.) C.) D.) E.) iRespond Question F Fill-In 1AC8100C-333F-1946-81F7-99DFFA5B1A6C x y 1 2 14 3 98 4 686 n A.) 4802;; B.) C.) D.) E.)

Find the next term and write the recursive rule. y 1 2 14 3 98 4 686 n

Find the next term x y 1 19 2 13 3 7 4 n A.) -5;; B.) C.) D.) E.) F iRespond Question F Fill-In 9F1BD1C0-5A78-7944-AC32-52752F0B1A67 x y 1 19 2 13 3 7 4 n A.) -5;; B.) C.) D.) E.)

Find the next term and write the recursive rule. y 1 19 2 13 3 7 4 n

Write the explicit rule and the recursive rule. a1 = 15 and d = 5

Write the explicit rule and the recursive rule. a1 = 4 and r = 0.2

Arithmetic and Geometric Sequences Practice 7 tables Practice Worksheet Arithmetic and Geometric Sequences Practice 7 tables

Explicit and Recursive Sequences Practice 12 problems Homework Explicit and Recursive Sequences Practice 12 problems