9.1 Sequences and Series

 

Sequence: Function whose domain is the set of positive integers.

 

Finding the First Four Terms of a Sequence

1.     a_n=5n-3

a₁=5(1)-3=2

a₂=5(2)-3=7

a₃=5(3)-3=12

a₄=5(4)-3=17

2.     a_n=3 + (-2)ⁿ

a₁=3 + (-2)¹ = 1

a₂=3 + (-2)² = 7

a₃=3 + (-2)³ = -5

a₄=3 + (-2)⁴ = 19

Finding the nth Term of a Sequence

      1.     2, 8, 18, 32, …

Each term is twice the square of n

2n²



Factorials

n! = (1) (2) (3) (4) (5) ... (n-1) (n)

 

Using Factorials

1.     5!

(5) (4) (3) (2) (1)

120

 2.

 

 

 

Series: Sum of the terms of an infinite sequence.

 

Finding the Sum of a Series