1. Module 3 Arithmetic and Geometric Sequences

2. Module 3.2 Arithmetic and Geometric Sequences

4. 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

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

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

9. 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

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