Pre-Algebra 12-1 Arithmetic Sequences Learn to find terms in an arithmetic sequence.

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Presentation transcript:

Pre-Algebra 12-1 Arithmetic Sequences Learn to find terms in an arithmetic sequence.

Pre-Algebra 12-1 Arithmetic Sequences A sequence is a list of numbers or objects, called terms, in a certain order. In an arithmetic sequence, the difference between one term and the next is always the same. This difference is called the common difference. The common difference is added to each term to get the next term.

Pre-Algebra 12-1 Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. A. 5, 8, 11, 14, 17,... Example 1: Identifying Arithmetic Sequences Find the difference of each term and the term before it. The sequence could be arithmetic with a common difference of ,

Pre-Algebra 12-1 Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. C. 65, 60, 55, 50, 45,... Example 3: Identifying Arithmetic Sequences The sequence could be arithmetic with a common difference of –5. Find the difference of each term and the term before it ,... –5

Pre-Algebra 12-1 Arithmetic Sequences Writing Math Subscripts are used to show the positions of terms in the sequence. The first term is a 1, the second is a 2, and so on. FINDING THE n th TERM OF AN ARITHMETIC SEQUENCE The n th term a n of an arithmetic sequence with common difference d is a n = a 1 + (n – 1)d.

Pre-Algebra 12-1 Arithmetic Sequences Find the given term in the arithmetic sequence. A. 10 th term: 1, 3, 5, 7,... Example 4: Finding a Given Term of an Arithmetic Sequence a n = a 1 + (n – 1)d a 10 = 1 + (10 – 1)2 a 10 = 19

Pre-Algebra 12-1 Arithmetic Sequences Find the given term in the arithmetic sequence. B. 18 th term: 100, 93, 86, 79,... Example 5: Finding a Given Term of an Arithmetic Sequence a n = a 1 + (n – 1)d a 18 = (18 – 1)(–7) a 18 = -19

Pre-Algebra 12-1 Arithmetic Sequences Find the given term in the arithmetic sequence. C. 21 st term: 25, 25.5, 26, 26.5,... Example 6: Finding a Given Term of an Arithmetic Sequence a n = a 1 + (n – 1)d a 21 = 25 + (21 – 1)(0.5) a 21 = 35

Pre-Algebra 12-1 Arithmetic Sequences Find the given term in the arithmetic sequence. D. 14 th term: a 1 = 13, d = 5 Example 7: Finding a Given Term of an Arithmetic Sequence a n = a 1 + (n – 1)d a 14 = 13 + (14 – 1)5 a 14 = 78