Warm Up 1st Term:___ 1st Term:_ 2nd Term:_ 2nd Term:___

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Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____ Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula. a 1 = 28, d = 10 2) a 1 = −38, d = −100 1st Term:_____ 2nd Term:_____ 3rd Term:_____ 4th Term:_____ 5th Term:_____ 1st Term:_____ 2nd Term:_____ 3rd Term:_____ 4th Term:_____ 5th Term:_____

Let’s Take it up a notch Given a term in an arithmetic sequence and the common difference find the first term and the explicit formula. 1) a 38 = −53.2, d = −1.1 2) a 40 = −1191, d = −30

Warm Up(Answers) An = d(n-1) + a1 1st Term: 28 An = 10(n-1) + 28 Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula. a 1 = 28, d = 10 2) a 1 = −38, d = −100 An = d(n-1) + a1 An = 10(n-1) + 28 Or = 10n – 10 +28 = 10n + 18 An =10n + 18 An = d(n-1) + a1 An = -100(n-1) - 38 Or = -100n + 100 -38 = -100n + 62 An =-100n + 62 1st Term: 28 2nd Term: 28 +10 = 38 3rd Term: 48 +10 = 48 4th Term: 48 +10 = 58 5th Term: 58 +10 = 68 1st Term: -38 2nd Term: -38 -100 = -138 3rd Term:-138 -100 = -238 4th Term:-238 -100 = -338 5th Term:-338 -100 = -438

Let’s Take it up a notch (Answers) Given a term in an arithmetic sequence and the common difference find the first term(a 1) and the explicit formula. 1) a 38 = −53.2, d = −1.1 2) a 40 = −1191, d = −30 An = d(n-1) + a1 A38 = -1.1(n-1) + a1 A38 = -1.1(38-1) + a1 -53.2= -1.1(37) + a1 -53.2 =-40.7 + a1 + 40.7 +40.7 12.5 = a1 a1 = 12.5 d= -1.1 An = d(n-1) + a1 An = -1.1(n-1) + 12.5 Or = -1.1n + 1.1 +28 = -1.1n + 29.1 An = -1.1n + 29.1 An = d(n-1) + a1 A40 = -30(n-1) + a1 A40 = -30(40-1) + a1 -1191= -30(39) + a1 -1191 =-1170 + a1 + 1170 +1170 -21 = a1 a1 = -21 d= -30 An = d(n-1) + a1 An = -30(n-1) – 21 or An = -30(n-1) - 21 = -30n +30 -21 = -30n + 9 An = -30n + 9