Mathematics - Generating Patterns, Slides of Mathematics

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Objectives

write the rule for the nth term of a sequence

find the nth term of a sequence; and generate pattern from a given succession of objects, numbers, letters, or symbols;

Generating Patterns

Activity 1: What’s Next?

1. What is the next shape?

---

3. What is the next number?

What is the 8

th

number?

9, 4, -1, -6, -11, ___ ,…, ___-16 (^) -

4. What is the next number?

What is the 12

th

number?

1, 3, 9, 27, 81, ____ ,…,

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243 177147

What is a A sequence sequence? is a function

whose domain is the finite set

{1, 2, 3, …, n} or the infinite

set {1, 2, 3, …}. It also means

an ordered list.

Each number or element in a

sequence is called a term.

Domain n

Range A𝑛

1 st Term 2 nd Term 3 rd Term 4 th Term 5 th Term 𝐴 1 𝐴 2 𝐴 3 𝐴 4 𝐴 5

2. Give numbers which are all

divisible by 7.

7, 14, 21, 28, 35, …

Finite sequence Infinite sequence

It is a finite sequence

because it has a last

term, which is 20.

It is an infinite

sequence because it

has no last term,

which means it

continues infinitely.

Example:

Write the first 5 terms of

Domain 1 2 3 4 5 Range General Rule 𝑨 𝒏 = 𝟐 𝒏 wherein: n is the term number is the nth term

𝒏

𝟏

𝟏

𝟐

𝟐

𝟑

𝟑

𝟒

𝟒

𝟓

𝟓

Write the first 5 terms of.

Domain 1 2 3 4 5 Range General Rule 𝑨 𝒏 = 𝟑 ¿ Solution:

𝒏

𝟏

𝟏

𝟏

𝟏

𝟐

𝟐

𝟐

𝟐

𝟑

𝟑

𝟑

𝟑

𝟒

𝟒

𝟒

𝟒

𝑨 𝟓 = 𝟑 ¿

𝟓

𝟓

𝟓

3 6 12 24 48

Your

turn!

Activity 2: Term after Term