Arithmetic Progressions “AP’s” & “GP’s” Geometric Progressions

Arithmetic Progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. Example : 1 , 5 , 9 , 13 5 – 1 = 9 -5 = 13 – 9 This will help us fill in blanks in an AP

Example What is the 32nd term of 5 , 11 , 17 , 23 ….

Example 5+4d=3 Fill in the blanks on the AP: 2 Ways to solve: - Solve using the “d” value and an equation - Insert Arithmetic Means 5+4d=3

Example Which term of 4 , 16 , 28 , …… is 328?

Geometric Progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. 1, 5, 25, 125,….. Where 1/5=5/25=25/125

Example What is the 6th term of 3/5 , 3 , 15 , 75 ….

Example Fill in the blanks on the GP: - Create an equation with the common ratio

Example Find the sum of the first 26 terms of the AP. -5 , -1 , 3 , 7 ,…… We are missing

Example Find the sum of: -Substitute 2 for k to solve for “a” -Subtract 2 from 40 and add 1 to find the number of terms. -Substitute 40 for k to solve for -Find “d” by finding the second term and subtract from first term.

Example Solve: Find the sum of the following

Example Find all the values of x so that Are consecutive terms of an GP. - Set up 2 equations, any ideas? 1st term/2nd term=2nd term/3rd term (GP’s have a ratio) 1 , 3 , 9 1/3 = 3/9

Example Insert two numbers between 2 and 20 so that the first three numbers form a GP while the last three numbers form an AP

Group Problem Homework Assignment # 6 The 3rd term of an AP is 6. The 2nd, 4th and 7th terms of the AP form the first three terms of a GP. Find the first term of the AP Homework Assignment # 6