Generating-Patterns: Arithmetic Sequences, Arithmetic Mean,

Generating Arithmetic patterns

1. Mathematics 10 A Mrs. Kassandra Venzuelo-Alayon

2. Draw the next object in each picture pattern. WHAT'S NEXT?

3. Generating Patterns

4. Sequence A sequence is a set of objects which is listed in a specific order, one after another. Each member or element in the sequence is called term .

5. Finite Sequence A finite sequence contains a limited number of terms. This means it has an end or last term. Consider the examples below. a) Days of the week: (Monday, Tuesday, ..., Sunday) b) First 10 positive perfect squares: 1, 4, 9, 16, 25, 36, 49, 64,81, 100)

6. Infinite Sequence On the other hand, an infinite sequence contains a countless number of terms. The number of terms of the sequence continues without stopping or it has no end term. The ellipsis (...) shows that a sequence is infinite. a. Counting Numbers: (1, 2, 3, 4, 5...)

7. Write the general term of the sequence 2, 4, 8, 16, 32, ...

8. Identify the Pattern Look at the following sequence. Is there a specific pattern for each?

9. Arithmetic Sequence The constant number being added is called the common difference and is represented as d. All these sequences are called arithmetic sequences.

10. Finding the nth term In the arithmetic sequence: 3, 8, 13, 18, ..., What is the 15th term?

11. Arithmetic Mean The first and last terms of a finite arithmetic sequences are called arithmetic extremes, and the terms in between are called arithmetic means.

12. Finding the sum of the first n terms of an Arithmetic Sequence

13. Arithmetic Series An arithmetic series is a series related sequence is arithmetic. It results from adding the terms of an arithmetic sequence .