1. Warm Up

2. 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

3. 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

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