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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. - PowerPoint PPT Presentation

10.2Arithmetic SequencesDate: ____________

Arithmetic SequenceSequence 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, . . .+3+3+3+316, 14, 12, 10, 8, . . .-2 -2 -2 -2Common 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 = 44, 5, 7, 10, 14,No.1, 4, 8, 12, 16,No.-4, -7, -10, -13, -16,Yes.d = -3

Arithmetic Sequencean = a1 + d(n 1)

an = nth term of the sequencea1 = first termn = # of termsd = common difference

Find an and a20.a1 = 7d = 5an = 7 + 5(n 1)an = 7 + 5n 5 an = 2 + 5na20 = 2 + 5(20) a20 = 102 an = a1 + d(n 1)

Find an and a25.48, 53, 58, 63,an = a1 + d(n 1)485an = 48 + 5(n 1)an = 48 + 5n 5 an = 43 + 5na25= 43 + 5(25)a25 = 168

Find an and a25.-21, -39, -57, -75,an = a1 + d(n 1)-21-18an = -21 18(n 1)an = -21 18n + 18 an = -3 18na25= -3 18(25)a25 = -453

Find an and a20.a17 = 22d = -4an = a1 + d(n 1)22 = a1 4(17 1)22 = a1 4(16)22 = a1 64 86 = a1an = 86 4(n 1)an = 86 4n +4 an = 90 4na20 = 90 4(20) a20 = 10

Find an and a13.a15 = 10a20 = 25d =25 10 20 15 =15 5 = 3an = a1 + d(n 1)10 = a1 + 3(15 1)10 = a1 + 3(14)10 = a1 + 42-32 = a1an = -32 + 3(n 1)an = -32 + 3n 3 an = -35 + 3na13 = -35 + 3(13) a13 = 4

Find an and a13.a12 = -23a27 = 37d =37 23 27 12 =60 15 = 4an = a1 + d(n 1)-23 = a1 + 4(12 1)-23 = a1 + 4(11)-23 = a1 + 44-67 = a1an = -67 + 4(n 1)an = -67 + 4n 4 an = -71 + 4na13 = -71 + 4(13) a13 = -19

Sum of a Finite Arithmetic SequenceFind the sum of the first 10 terms of the sequence if a1 = -16 and a10 = 20S10 = 20

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

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 = 302S100 = 15,350

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 = -142S24 = -1752

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

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