Module 3 Arithmetic and Geometric Sequences

Module 3.2 Arithmetic and Geometric Sequences

Arithmetic Sequence Formulas Recursive Formula Explicit Formula 𝒇 𝟏 = _________ 𝒇 𝒕 = 𝒅 𝒕 +𝒇 𝟎 𝒇 𝒕 =𝒇 𝒕−𝟏 +𝒅 𝒇 𝒙 =𝒎𝒙+𝒃 𝒇 𝟏 𝒊𝒔 𝒇𝒊𝒓𝒔𝒕 𝒕𝒆𝒓𝒎 𝒅 𝒊𝒔 𝒔𝒍𝒐𝒑𝒆 𝒇 𝟎 𝒊𝒔 𝒚−𝒊𝒏𝒕 𝒅 𝒊𝒔 𝒘𝒉𝒂𝒕 𝒚𝒐𝒖 𝒂𝒓𝒆 𝒂𝒅𝒅𝒊𝒏𝒈 𝒐𝒓 𝒔𝒖𝒃𝒕𝒓𝒂𝒄𝒕𝒊𝒏𝒈

Arithmetic Sequence Formulas Recursive Formula Explicit Formula 𝒇 𝟎 =𝟏 𝒇 𝒕 =𝒇 𝒕−𝟏 +𝟒 𝒇 𝒕 =𝟒𝒕+𝟏

Recursive Formula 𝑓 0 =3 𝑓 𝑡 =𝑓(𝑡−1)(2) Explicit Formula 𝑓 𝑥 =3 (2) 𝑡

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

HW 3.2 #1-14 and 3.3 #1-9