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Arithmetic Sequence Formulas Recursive Formula Explicit Formula 𝒇 𝟏 = _________ 𝒇 𝒙 = 𝒅 𝒙 +𝒇 𝟎 𝒇 𝒙 =𝒇 𝒙−𝟏 +𝒅 𝒇 𝒙 =𝒎𝒙+𝒃 or 𝒇 𝒙 =𝒇 𝟏 +𝒅(𝒙−𝟏) 𝒇 𝟏 𝒊𝒔 𝒇𝒊𝒓𝒔𝒕 𝒕𝒆𝒓𝒎 𝒅 𝒊𝒔 𝒔𝒍𝒐𝒑𝒆 𝒇 𝟎 𝒊𝒔 𝒚−𝒊𝒏𝒕 𝒅 𝒊𝒔 𝒕𝒉𝒆 𝒄𝒐𝒎𝒎𝒐𝒏 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆

𝑓 1 = ______ 𝑓 𝑥 =𝑓(1) (𝑟) (𝑥−1) 𝑓 𝑥 =𝑓 𝑥−1 (𝑟) or 𝑓 𝑥 =𝑓(0) (𝑟) 𝑥 Recursive Formula Explicit Formula 𝑓 1 = ______ 𝑓 𝑥 =𝑓(1) (𝑟) (𝑥−1) 𝑓 𝑥 =𝑓 𝑥−1 (𝑟) or 𝑓 𝑥 =𝑓(0) (𝑟) 𝑥 a. 1, –6, 36, –216, . . . b. 2, 4, 6, 8, . . . Recursive Formula 𝑓 1 =1 𝑓 𝑥 =𝑓 𝑥−1 (−6) Explicit Formula 𝑓 𝑥 =1 (−6) (𝑥−1) Or 𝑓 𝑥 = −1 6 (−6) 𝑥

Essential Question: How are explicit formulas different then recursive formulas? What are the advantages of using an explicit formula versus a recursive formula?