Aim: What is the arithmetic sequence?

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Presentation transcript:

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

Each term after the first term is four more than the previous term 7, 11, 15, 19 Each term after the first term is four more than the previous term 4 4 4 The sequence an = 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: an = a1 + d(n – 1) Where d is the common difference

For the arithmetic sequence 100, 97, 94, 91,…, find : a) the common difference b) the 20th term of the sequence d = – 3 a20 = a1 + d(n – 1) = 100 + -3(20 – 1) = 100 + -3(19) = 100 – 57 = 43

The 4th term of an arithmetic sequence is 80 and the 12th term is 32. a. What is the common difference? b. What is the first term of the sequence? a. b. 80 = a1 + 3(-6), 80 = a1 – 18, a1 = 98

If 4 and 28 are the 1st and 5th terms of an arithmetic sequence, find the 2nd, 3rd and 4th 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.

Scott is saving to buy a guitar 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 a1 = 42 and d = 8 then an = 400 46th week

a. Find the common difference b. Write the nth term formula 1. Given an arithmetic sequence 3,6,9,12,…, n = 8 a. Find the common difference b. Write the nth term formula c. Find the value of 8th term d = 3 an = 3 + 3(n – 1) a8 = 24 2. Write the first six terms of the arithmetic sequence that has 12 for the first term and 42 for the six term. 12, 18, 24, 30, 36, 42 3. Find four arithmetic means between 3 and 18 6, 9, 12, 15