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10.2 Arithmetic Sequences

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. +3. +3. +3. +3. Common difference is 3. 5, 8, 11, 14, 17,. (d = 3). -2. -2. -2. -2.

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10.2 Arithmetic Sequences

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  1. 10.2Arithmetic Sequences Date: ____________

  2. Arithmetic Sequence • Sequence in which each term after the first is obtained by adding a fixed number, called the difference, to the previous term. +3 +3 +3 +3 Common difference is 3. 5, 8, 11, 14, 17, . . . (d = 3) -2 -2 -2 -2 Common difference is -2. 16, 14, 12, 10, 8, . . . (d = -2)

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

  4. Arithmetic Sequence an = a1 + d(n − 1) an = nth term of the sequence a1 = first term n = # of terms d = common difference

  5. Find an and a20. a1 = 7 d = 5 an = a1 + d(n − 1) an = 7 + 5(n − 1) an = 7 + 5n – 5 an = 2 + 5n a20 = 2 + 5(20) a20 = 102

  6. Find an and a25. 48, 53, 58, 63,… an = a1 + d(n − 1) 48 5 an = 48 + 5(n – 1) an = 48 + 5n – 5 an = 43 + 5n a25 = 43 + 5(25) a25 = 168

  7. Find an and a25. -21, -39, -57, -75,… an = a1 + d(n − 1) -21 -18 an = -21 – 18(n – 1) an = -21 – 18n + 18 an = -3 – 18n a25 = -3 – 18(25) a25 = -453

  8. Find an and a20. a17 = 22 d = -4 an = a1 + d(n − 1) an = 86 – 4(n − 1) 22 = a1 – 4(17 − 1) an = 86 – 4n +4 an = 90 – 4n 22 = a1 – 4(16) a20 = 90 – 4(20) 22 = a1 – 64 a20 = 10 86 = a1

  9. Find an and a13. 25 – 10 15 a15 = 10 a20 = 25 d = = = 3 20 – 15 5 an = a1 + d(n − 1) an = -32 + 3(n − 1) 10 = a1 + 3(15 − 1) an = -32 + 3n – 3 10 = a1 + 3(14) an = -35 + 3n 10 = a1 + 42 a13 = -35 + 3(13) -32 = a1 a13 = 4

  10. Find an and a13. 37 − ‾23 60 a12 = -23 a27 = 37 d = = = 4 27 – 12 15 an = a1 + d(n − 1) an = -67 + 4(n − 1) -23 = a1 + 4(12 − 1) an = -67 + 4n – 4 -23 = a1 + 4(11) an = -71 + 4n -23 = a1 + 44 a13 = -71 + 4(13) -67 = a1 a13 = -19

  11. ( ) ( ) Sum of a Finite Arithmetic Sequence Find the sum of the first 10 terms of the sequence if a1 = -16 and a10 = 20 S10 = 20

  12. Find the sum of the first 42 terms of the sequence if a1 = 7 and a42 = 239 ( ) ( ) S42 = 5166

  13. ( ) ( ) Find the sum of the first 100 terms of the sequence if a1 = 5 and d = 3. an = a1 + d(n − 1) a100 = 5 + 3(100 − 1) a100 = 302 S100 = 15,350

  14. ( ) ( ) Find the sum of the first 24 terms of the sequence if a1 = -4 and d = -6. an = a1 + d(n − 1) a24 = -4 – 6(24 − 1) a24 = -142 S24 = -1752

  15. Find the sum of the first 50 terms of the sequence 34, 45, 56, 67, 78,… ( ) ( ) an = a1 + d(n − 1) a50 = 34 + 11(50 − 1) a50 = 573 S50 = 15,175

  16. ( ) ( ) Find the sum of the first 20 terms of the sequence 12, 18, 24, 30, 36,… an = a1 + d(n − 1) a20 = 12 + 6(20 − 1) a20 = 126 S20 = 1380

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