10.2 Arithmetic Sequences Date: ____________. Arithmetic Sequence Sequence in which each term after the first is obtained by adding a fixed number, called.

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Presentation transcript:

10.2 Arithmetic Sequences Date: ____________

Arithmetic Sequence Sequence in which each term after the first is obtained by adding a fixed number, called the difference, to the previous term. 5, 8, 11, 14, 17, , 14, 12, 10, 8, Common difference is 3. (d = 3) Common difference is -2. (d = -2)

Decide if each sequence is an arithmetic sequence. If yes, find the common difference. -5, -1, 3, 7, 11,... Yes.d = 4 4, 5, 7, 10, 14,… No. 1, 4, 8, 12, 16,… No. -4, -7, -10, -13, -16,… Yes.d = -3

Arithmetic Sequence a n = a 1 + d(n − 1) a n = n th term of the sequence a 1 = first term n = # of terms d = common difference

Find a n and a 20. a 1 = 7d = 5 a n = 7 + 5(n − 1) a n = 7 + 5n – 5 a n = 2 + 5n a 20 = 2 + 5(20) a 20 = 102 a n = a 1 + d(n − 1)

Find a n and a , 53, 58, 63,… a n = a 1 + d(n − 1) 485 a n = (n – 1) a n = n – 5 a n = n a 25 = (25) a 25 = 168

Find a n and a , -39, -57, -75,… a n = a 1 + d(n − 1) a n = -21 – 18(n – 1) a n = -21 – 18n + 18 a n = -3 – 18n a 25 = -3 – 18(25) a 25 = -453

Find a n and a 20. a 17 = 22d = -4 a n = a 1 + d(n − 1) 22 = a 1 – 4(17 − 1) 22 = a 1 – 4(16) 22 = a 1 – = a 1 a n = 86 – 4(n − 1) a n = 86 – 4n +4 a n = 90 – 4n a 20 = 90 – 4(20) a 20 = 10

Find a n and a 13. a 15 = 10a 20 = 25 d = 25 – – 15 = 15 5 = 3 a n = a 1 + d(n − 1) 10 = a 1 + 3(15 − 1) 10 = a 1 + 3(14) 10 = a = a 1 a n = (n − 1) a n = n – 3 a n = n a 13 = (13) a 13 = 4

Find a n and a 13. a 12 = -23a 27 = 37 d = 37 − ‾23 27 – 12 = = 4 a n = a 1 + d(n − 1) -23 = a 1 + 4(12 − 1) -23 = a 1 + 4(11) -23 = a = a 1 a n = (n − 1) a n = n – 4 a n = n a 13 = (13) a 13 = -19

Sum of a Finite Arithmetic Sequence ( ) Find the sum of the first 10 terms of the sequence if a 1 = -16 and a 10 = 20 ( ) S 10 = 20

Find the sum of the first 42 terms of the sequence if a 1 = 7 and a 42 = 239 ( ) S 42 = 5166 ( )

Find the sum of the first 100 terms of the sequence if a 1 = 5 and d = 3. ( ) a n = a 1 + d(n − 1) a 100 = 5 + 3(100 − 1) a 100 = 302 ( ) S 100 = 15,350

Find the sum of the first 24 terms of the sequence if a 1 = -4 and d = -6. ( ) a n = a 1 + d(n − 1) a 24 = -4 – 6(24 − 1) a 24 = -142 ( ) S 24 = -1752

Find the sum of the first 50 terms of the sequence 34, 45, 56, 67, 78,… ( ) a 50 = (50 − 1) a 50 = 573 ( ) S 50 = 15,175 a n = a 1 + d(n − 1)

Find the sum of the first 20 terms of the sequence 12, 18, 24, 30, 36,… ( ) a 20 = (20 − 1) a 20 = 126 ( ) S 20 = 1380 a n = a 1 + d(n − 1)