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4 – 6 Arithmetic Sequences WW: sequence, term, arithmetic sequence, common difference EQ: How is identifying an arithmetic sequence similar to identifying a function rule? When you list the times and distances in order, each list forms a sequence. A sequence is a list of numbers that often forms a pattern. Each number in a sequence is a term. When the terms of a sequence differ by the same nonzero number, the sequence is an arithmetic sequence. The difference between the terms is called the common difference. Determine whether each sequence is arithmetic, find the common difference if it is, and the next 3 terms Ex1) 12, 8, 4, 0, … -4 -4 -4 Arithmetic CD: -4 Ex2) 1, 4, 9, 16, … +3 +5 +7 Not arithmetic Next three: -4, -8, -12 You try 1)-¾, -¼, ¼, ¾, … 2)2/3, 1/3, -1/3, -2/3, … 3)-4, -2, 1, 5, … 4)4, 1, -2, -5, … Arith; CD: 1/2; 5/4, 7/4, 9/4 Not Arith Not Arith Arith; CD: -3; -8, -11, -14 Find the indicated term of the arithmetic sequence Ex3) 22nd term: 5, 2, -1, -4, … Step 1: Find the common difference: -3 Step 2: Write a rule to find the 22nd term an = a1 + (n – 1)d n = term number wanted a22= 5 + (22 – 1)(-3) a1 = the first term a22= 5 + (21)(-3) d = common difference a22= 5 + (-63) a22= -58 YT: 60th term: 11, 5, -1, -7, … YT: 15th term: a1 = 7; d = 3 a60 = 11 + (60 – 1)(-6) a15 = 7 + (15 – 1)(3) a60 = 11 + (59)(-6) a15 = 7 + (14)(3) a60 = 11 + (-354) a15 = 7 + (42) a60 = -343 a15 = 49 The odometer on a car reads 60,473. Every day the car is driven 54 miles. What is the odometer reading 20 days later? Step 1: Find d, a1, and n. d = 54, a1 = 60,473, n = 21 a21 = 60,473 + (21 – 1)(54) a21 = 60,473 + (20)(54) a21 = 60,473 + (1080) a21 = 61,553 miles YT: Each time a truck stops, it drops off 250 pounds of cargo. It started with a load of 2000 pounds. How much does the load weigh after the fifth stop? d = -250, a1 = 2000, n=6 a5 = 2000 + (6 – 1)(-250) a5 = 2000 + 5(-250) a5 = 2000 + (-1250) a5 = 750 lbs Answer EQ: You must find the difference from one number to the next and turn it into an equation.