1. Sequences and Summation Notation. What you’ll learn Find particular terms of a sequence from the general term. Use recursion formulas. Use factorial notation. Use summation notation. Remember

2. Many creations in nature involve intricate mathematical designs, including a variety of spirals. For example, the arrangement of the individual florets in the head of a sunflower forms spirals. In some species, there are 21 spirals in the clockwise direction and 34 in the counterclockwise direction. The precise numbers depend on the species of sunflower: 21 and 34, or 34 and 55, or 55 and 89, or even 89 and 144 The Fibonacci sequence of numbers is an infinite sequence that begins as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,..... The first two terms are 1. Every term thereafter is the sum of the two preceding terms. We can think of the Fibonacci sequence as a function. The terms of the sequence are the range values for a function whose domain is the set of positive integers. Domain: 1, 2, 3, 4, 5, 6, 7,… Range: 1, 1, 2, 3, 5, 8, 13,... f(1) = 1, f(2) = 1, f(3) = 2,

3. Answer a) Answer b)

4. Recursion Formulas Answer

5. Factorial Notation Products of consecutive positive integers occur quite often in sequences. These products can be expressed in a special notation, called factorial notation.

6. Answer

8. Summation Notation The Cost of Raising a Child Born in the U.S. in 2006 to a Middle-Income Family

9. When we write out a sum that is given in summation notation, we are expanding the summation notation.

10. Answer

12. Properties of Sums