The student will identify and extend geometric and arithmetic sequences.

6.17 Vocabulary pg- Numerical patterns may include linear and exponential growth, perfect squares, triangular and other polygonal numbers, or Fibonacci numbers. Arithmetic and Geometric sequences are types of numerical patterns. Arithmetic sequence, determine the difference, called the common difference, between each succeeding number in order to determine what is ADDED to each previous number to obtain the next number. Sample numerical patterns are 6, 9, 12, 15, 18, …; and 5, 7, 9, 11, 13, …. Geometric number patterns, determine what each number is MULTIPLIED by to obtain the next number in the geometric sequence. This multiplier is called the common ratio. Sample geometric number patterns include 2, 4, 8, 16, 32, …; 1, 5, 25, 125, 625, …; and 80, 20, 5, 1.25, … ***Geometric patterns may involve shape, size, angles, transformations of shapes, and growth. Common ratio The ratio used to determine what each number is multiplied by in order to obtain the next number in the geometric sequence Common difference The difference between each succeeding number in order to determine what is added to each previous number to obtain the next number in a arithmetic pattern. Triangular number- A triangular number can be represented geometrically as a certain number of dots arranged in a triangle, with one dot in the first (top) row and each row added having one more dot that the row above it. To find the next triangular number, a new row is added to an existing triangle. The first row has 1 dot, the second row 2 dots, the third row 3 dots and so on. So add = 6 or just count all the dots. Square Number- A square number can be represented geometrically as the number of dots in a square array. Square numbers are perfect squares and are the numbers that result from multiplying any whole number by itself (e.g., 36 = 6  6). Powers of , 10, 100, 1,000, 10,000 (just count the zeros and that is your power) Consecutive- Following one after the other in order. Strategies to recognize and describe the differences between terms in numerical patterns include, but are not limited to, examining the change between consecutive terms, and finding common factors. An example is the pattern 1, 2, 4, 7, 11, 16,… Pg 6.17 practice POWERS OF TEN (just count the zeroes and that is your power) 10 1 = = 1, = __________ Triangular Numbers, just add a row to the bottom. What is the number in the 8 th position? 1 ST term 2 ND term 3 RD term 4 TH term 6 TH 7 TH 8 TH Perfect squares! What is the number in the 6 th position? ST term 2 ND term 3 RD term 4 TH 5 TH 6 TH ____ _____ ______ Fibonacci Sequence! Each number is the sum of the previous two numbers. Name the 12 th term. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ____, ____ 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th 11 th 12 th Find the common difference or common ratio and name as an arithmetic or geometric pattern 64, 16, 4, 1 ____________ rule?___________ 25, 30, 35, 40 _____________ What is the tenth shape? x y