Lesson 3.10: Introduction to Sequences Concept: Recognizing Sequences EQ: How do we recognize and describe patterns? (F.IF.3, F.LE.1) Vocab: Sequence, Term, Finite, Infinite, Fibonacci’s Sequence, Arithmetic Sequence, Geometric Sequence

Activator Look at the problems below. Try to figure out a pattern and write what comes next. 1, 7, 13, 19, … 2, 10, 50, 250, … 1, 4, 9, 25, 36, … , , , … 1, 1, 2, 3, 5, 8, 13, 21, …

Sequence - A list of numbers or objects in a special order. Each value in the sequence is called a term. A sequence can be infinite (with no end) or finite (ends). A sequence can be written as a function. We use An, Un, etc. to represent sequences n acts like the input or x-value (x) An acts like the output or y-value (f(x)) A3 is another way to say the third term The domain of the function that generates a sequence is all whole numbers.

Sequences continued… We will work with two types of sequences: Arithmetic- a sequence that increases or decreases by a constant rate (you add or subtract) Geometric- a sequence that increases or decreases by a factor (you multiply)

Example 1: An = 1, 3, 5, 7, …. Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Tell if the sequence is finite or infinite. Find the next term. Find the second term. Find A4.

Example 2: An = 2, 4, 8, 16. Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Tell if the sequence is finite or infinite. Find the second term. Find A3.

Example 3: An = 1, 1, 2, 3, 5, 8, … Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Tell if the sequence is finite or infinite. Find the next term. Find the second term. Find A3.

You Try 1: An = 0, 5, 10, 15, __, 25. Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Tell if the sequence is infinite or finite. Find the next term. Find the second term. Find A5.

Example 4: n 1 2 3 4 5 An 12 8 ? Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Find the next term. Find the second term. Find A5.

Example 5: n 1 2 3 4 5 An 17 15 10 8 ? Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Find the next term. Find the second term. Find A5.

You Try 2: n 1 2 3 4 5 An 27 9 ? Describe the pattern and identify if the sequence is arithmetic or geometric or neither. Find the next term. Find the second term. Find A5.

Summary 1.Create your own sequence. Be sure to record the pattern you used to create your sequence, but do not show your partner. 2. Trade your sequence with your partner and see if they can figure out your pattern. Video for Activity: http://www.youtube.com/watch?v=ahXIMUkSXX0