2. Aim: What is the arithmetic sequence? Do Now: Find the first four terms in the sequence whose n th term is 4n + 3. HW: p.256 # 4,5,6,8,10,12,16,18,19,20

3. 7, 11, 15, 19 444 Each term after the first term is four more than the previous term The sequence a n = 4n + 3 is an arithmetic sequence. An arithmetic sequence has consecutive terms with a common difference. In this case, the common difference is 4. For an arithmetic sequence, the recursive formula is: a n = a 1 + d(n – 1) Where d is the common difference

4. For the arithmetic sequence 100, 97, 94, 91,…, find : a) the common difference b) the 20 th term of the sequence d = – 3 a 20 = a 1 + d(n – 1)= 100 + -3(20 – 1) = 100 + -3(19) = 100 – 57 = 43

5. The 4 th term of an arithmetic sequence is 80 and the 12 th term is 32. a. What is the common difference? b. What is the first term of the sequence? a. b. 80 = a 1 + 3(-6), 80 = a 1 – 18, a 1 = 98

6. If 4 and 28 are the 1 st and 5 th terms of an arithmetic sequence, find the 2 nd, 3 rd and 4 th terms of the sequence. Use the recursive formula to find d The numbers 10, 16 and 22 are called arithmetic means between 4 and 28. An arithmetic mean is the average of the term before it and the term after it.

7. Scott is saving to buy a guitar. In the first week, he put aside $42 that he received for his birthday, and in each of the following weeks, he added $8 to his savings. He needs $400 for the guitar that he wants. In which week will he have enough money for the guitar? Let a 1 = 42 and d = 8 then a n = 400 46 th week

8. a. Find the common difference b. Write the n th term formula 1. Given an arithmetic sequence 3,6,9,12,…, n = 8 2. Write the first six terms of the arithmetic sequence that has 12 for the first term and 42 for the six term. 3. Find four arithmetic means between 3 and 18 d = 3a n = 3 + 3(n – 1) 12, 18, 24, 30, 36, 42 6, 9, 12, 15 c. Find the value of 8 th term a 8 = 24