1. Module 3 Arithmetic and Geometric Sequences

2. Module 3.2 Arithmetic and Geometric Sequences

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

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

8. 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