Sequences - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Sequences A sequence is a set of numbers that are in order Example And, each number of a sequence is called term of the sequence There are two types of sequences Infinite Sequences These go on forever (indicated by the three dots ... at the end) Finite Sequences These have a specific number of terms and then stop (like the sequence 6, 12, 24, 48, 96) Examples of some sequences are Let’s see how we denote terms in a sequence Here, 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 5, 7, 9, 11, 13, ... 1, 3, 6, 10, 15, 21, 28, ... 1, 4, 9, 16, 25, 36, 49, ... (Natural numbers) (Odd numbers) (Triangular numbers) (Square Number) 𝒕_𝟏 means first term 𝒕_𝟐 means second term 𝒕_𝟑 means third term 𝒕_𝟒 means fourth term And so on Note Sequences aren't just whole positive numbers. They can decrease, they can contain negative numbers (like --7, –3, 1, 5, 9…), or they can contain decimals that get progressively smaller (like 1, 0.5, 0.33, 0.25…)