## Explicit Expressions and Recursive Processes

#### Aligned To Common Core Standard:

**High School Building Functions** - HSF-BF.A.1a

What Are Explicit Expressions and Recursive Processes?
Are you unaware of explicit expressions and recursive processes, then don't worry, we'll take a look at what they mean one by one.
**Explicit Expressions** - Have you seen a stop sign? It tells us to put a halt to our driving or stop driving for a while. It clearly explains what we need to do. Similar to that, explicit expressions clearly explain or are expressed clearly. Hence, they are quite easy to understand and apply. To be more precise, explicit expressions are functions that are written in terms of input or independent variables.
**Recursive Processes** - Let's say you are given a sequence that represents numbers 1, 2, 4, 8, 16, and so on. We can easily figure out that there is a pattern being followed here, which is the original number being doubled that produces the next number. The method of applying the formula over and over is known as a recursive process.
These worksheets will help students identify and understand the use of both explicit expressions and recursive formulas.

### Printable Worksheets And Lessons

- Basic Sequences
Step-by-step Lesson- You are given a 2s sequence and asked to
provide two formats of the process.

- Guided Lesson
- If you understand the terms that are being presented, this is
not that difficult.

- Guided Lesson Explanation
- Make sure to check inverses when you are working with recursive
formulas.

- Practice Worksheet
- We switch between the formats. A good idea is to quiz them on
the format differences as well.

- Matching Worksheet
- See if you can match the parts of each format with the other.

#### Homework Sheets

Start with the recursive or explicit formula and find the other.

- Homework 1 - Write an explicit and recursive formula for the following sequences.
- Homework 2 - A recursive formula is a something that we can use to determine the next term in a set or number sequence. It tells us how each term is connected to the next term.
- Homework 3 - Given the recursive formula, write the explicit formula for the sequence.

#### Practice Worksheets

Explicit formulas give you the direct answer. The recursive formula gives you the next value.

- Practice 1 - Write an explicit and recursive formula for the following sequences: 1, 3, 5, 7...
- Practice 2 - Create both forms for: t
_{1}= 0 and t_{n}= t_{n-1}- 8 - Practice 3 - These are in the form of an equation.

#### Math Skill Quizzes

Work off what the problem gives you.