Week 5 Warm Up { -3, 8, 19, 30, 41, . . } n = 3 1) tn = 2) tn - 1 =

Slides:

Advertisements

Similar presentations

I can identify and extend patterns in sequences and represent sequences using function notation. 4.7 Arithmetic Sequences.

Advertisements

11.3 – Geometric Sequences.

Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….

Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.

Week 4 Warm Up ) Geometric or Arithmetic? -2, 4, -8, 16, -32, 64,…

Acc. Coordinate Algebra / Geometry A Day 36

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Algebra II Chapter : Use Recursive Rules with Sequences and Functions HW: p (4, 10, 14, 18, 20, 34)

Writing equations given 2 points on the line. Write the equation of the line that goes through the points (1, 6) and (3, -4) m = y₂ - y₁ x₂ - x₁ -4 -

Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.

Review of Sequences and Series

Se quences Recursive Definition Ch. 13 (2). Warm Up Find the first 4 terms of the sequence. State whether it is arithmetic, geometric or neither

Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2.

Warm Up Week 4 ( 2, 5 ) and ( 14, 1 ) 1) What is the midpoint?

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

Warm Up: On a sheet of paper Write the explicit formula for the sequence.

Warm up Write the exponential function for each table. xy xy

Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.

Warm Up Week 4 1) What is the distance between the sequence of numbers? -2, 4, 10, 16, 22,...

Day 9 Geometry.

Given an arithmetic sequence with

Review Find the explicit formula for each arithmetic sequence.

4-7 Arithmetic Sequences

Writing Linear Equations

Welcome! Grab a set of interactive notes Begin Working Let’s Recall

3.5 Arithmetic Sequences as Linear Functions

Geometry Creating Line Equations Part 1

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

Week 7 Warm Up solve when x = 3 x3 - 2 a) 5 b) -5 c) ±5 d) 25

What comes Next? Lesson 3.11.

Is the sequence arithmetic, geometric, or neither

Patterns & Sequences Algebra I, 9/13/17.

Module 1 Day 1 Evaluating Functions.

7-8 Notes for Algebra 1 Recursive Formulas.

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

Arithmetic Sequences.

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

11.3 – Geometric Sequences.

Warm up Write the exponential function for each table. x y x

11.3 – Geometric Sequences.

Geometric Sequences.

Coordinate Algebra Day 54

Warm Up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)

Arithmetic Sequences as functions

Geometric Sequences.

Notes Over 11.5 Recursive Rules

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

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

New EQ: How are sequences like functions?

Forms of a linear equation

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

Explicit formulas Sequences: Lesson 3.

Geometric Sequences A geometric sequence is a list of numbers with a common ratio symbolized as r. This means that you can multiply by the same amount.

Module 3 Arithmetic and Geometric Sequences

Write the recursive and explicit formula for the following sequence

EXPLICIT RULES: INPUT-OUTPUT FORMULAS

Classwork: Explicit & Recursive Definitions of

Homework: Explicit & Recursive Definitions of

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

Arithmetic Sequence A sequence of terms that have a common difference (d) between them.

Module 3 Arithmetic and Geometric Sequences

4-7 Arithmetic Sequences

1.6 Geometric Sequences Geometric sequence: a sequence in which terms are found by multiplying a preceding term by a nonzero constant.

Warm Up Write the first 4 terms of each sequence:

Lesson – How do Recursive Sequences Work? - Recursive Sequences

Lesson 6.7 Recursive Sequences

Presentation transcript:

Week 5 Warm Up 09.12.11 { -3, 8, 19, 30, 41, . . } n = 3 1) tn = 2) tn - 1 = 3) t6 =

Recursive Formula: Arithmetic if a3 = 10 then a3 - 1 = 7 d = 3 Recursive Formula: Arithmetic an = an - 1 + 3 a50 = a49 + 3

Geometry Sequences Day 5 I will write an explicit formula for an arithmetic sequence of numbers. Explicit Formula You Do not need to know the previous number to find a number in the sequence. an = dn + a0 Ex 1

Ex 2 • • • •

• • • • common difference? goes up by 3 common difference = slope Ex 2 output: 4, 7, 10, 13, • • • input: 1, 2, 3, 4 common difference? goes up by 3 common difference = slope

• • • • • y = mx + b Ex 3 y = x + 3 1 Explicit Formula an = 3n + 1

• • • • • • an = 3n + 1 an = 3n + 1 a3 = 3(3) + 1 a50 = 3(50) + 1 Ex 4 a3 = 3(3) + 1 a50 = 3(50) + 1 a3 = 9 + 1 a50 = 150 + 1 a3 = 10 a50 = 151

a = { 10, 8, 6, 4, 2,. . .} y = -2x + 12 tn = -2n + 12 t0 = -2(0) + 12 Ex 5 y = -2x + 12 Term # n Term tn 1 2 3 4 12 tn = -2n + 12 10 t0 = -2(0) + 12 8 6 t0 = 12 4 t0 = y-intercept

Explicit Formula: Arithmetic Sequence an = dn + a0 -2, 7, 16, 25, . . . Ex 6 d = 9 a0 = -11 an = 9n - 11

Handouts – 1.3 Day 1 Explicit Formulas What is the explicit formula? -6, 1, 8, 15, 22, . . . Assignment: Handouts – 1.3 Day 1 Explicit Formulas

a10 an = -2n + 12 a10 = -2( 10 ) + 12 a10 = -20 + 12 a10 = -8

• • • • • • an = 3n + 1 a0 = 3(0) + 1 a0 = 0 + 1 a0 = 1 Ex 5 a0 is the y-intercept a0 = 1

You have to know the previous number to find the next number. Recursive Formulas You have to know the previous number to find the next number. Arithmetic tn tn – 1 d = + Geometric = r ( ) tn-1 tn