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Arithmetic Sequence (1).notebook February 15, 2017 Arithmetic Sequences For this lesson, you will write everything that is in blue sequence a list of numbers in a special order arithmetic sequence a pattern formed by adding each term in a sequence by a fixed number called the common difference (d) ex: 7, 11, 15, 19,... recursion the process of describing a term (an) in a sequence in relation to the preceding term (an1) arithmetic recursive formula formula that tells how any term of an arithmetic sequence relates to the preceding term an = an1 + d What would be the recursive formula for the arithmetic sequence above? Arithmetic Sequence (1).notebook February 15, 2017 Find the recursive formula for each sequence and the next 3 terms. 1) 2, 9, 16, 23, ... 2) 5, 1, 3, 7, ... 3) 52, 41, 30, 19, ... What if you wanted to find any term? Arithmetic sequences are linear where the domain consists of natural numbers {1, 2, 3,...} and the range is the terms of the sequence arithmetic explicit formula formula that will work to find any term in an arithmetic sequence What do you think is the explicit formula for an arithmetic sequence? click y = mx + b Arithmetic Sequence (1).notebook February 15, 2017 II. Find the explicit formula for each sequence and the 20th term 1) 2, 9, 16, 23, ... 2) 5, 1, 3, 7, ... 3) 52, 41, 30, 19, ... Write a formula and find the 100th term of the following sequences. Pull 1. 2, 0, 2, 4,... 2. 4, 1, 2, 5,... -196 293 116.9 3. 8, 9.1, 10.2, 11.3, ... 1. Julia makes $2 an hour for her first hour of work, $4 her second hour, $6 the third hour and so on. How much money will she earn on her 12th hour of work? Arithmetic Sequence (1).notebook February 15, 2017 2. Hector gets better and better at a video game every time he plays. He scores 20 points in the first game, 25 in the second, 30 in the third and so on. How many points will he score in his 15th game? 3. Edgar is getting better at math. On his first test he scores 50 points, then he scores 53, 56, 59, 62 on his next 4 tests and his scores increase arithmetically thereafter. If he takes 20 tests, how many points will he earn on the last test? 4. Romo makes $12.00 an hour for his first hour of work, $17 his second hour, $22 his third hour and so on. How much money will he earn on his 50th hour of work? Arithmetic Word Problems 1. The sum of the interior angles of a triangle is 180 degrees, of a quadrilateral is 360, and a pentagon is 540 degrees. If the pattern continues, find the sum of the interior angles of a dodecagon (12 sides). 2. After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes each week. How many weeks will it be before you are up to jogging 60 minutes? 3. A theater has 60 seats in the first row, 68 in the second row, 76 in the third row, and so on. If the theater has 20 rows of seats, how many seats are in the 20th row? 4. What formula would you use to determine how many dots would be in the 50th figure? figure 1 figure 2 figure 3