Lesson 5 The Power of Negative Thinking Practice Understanding
The first and fifth terms of a sequence are given. Use what you know about arithmetic and geometric sequences to fill in the missing numbers. Identify the constant difference for the arithmetic sequences and the common ratio for the geometric sequences. Then write the explicit and recursive equations for each sequence.
1.
Arithmetic | |||||
|---|---|---|---|---|---|
Geometric |
Constant difference:
Common ratio:
Arithmetic recursive equation:
Arithmetic explicit equation:
Geometric recursive equation:
Geometric explicit equation:
2.
Arithmetic | |||||
|---|---|---|---|---|---|
Geometric |
Constant difference:
Common ratio:
Arithmetic recursive equation:
Arithmetic explicit equation:
Geometric recursive equation:
Geometric explicit equation:
3.
Arithmetic | |||||
|---|---|---|---|---|---|
Geometric |
Constant difference:
Common ratio:
Arithmetic recursive equation:
Arithmetic explicit equation:
Geometric recursive equation:
Geometric explicit equation:
Rewrite each problem so your answer has only positive exponents.
4.
Problem: | Step 1: | Step 2: | Answer: | |
|---|---|---|---|---|
a. | Rewrite with positive exponents. | Apply the exponent rules. | ||
b. | Rewrite with positive exponents. | Apply the exponent rules. |
5.
Problem: | Step 1: | Step 2: | Answer: | |
|---|---|---|---|---|
a. | ||||
b. |
6.
Problem: | Step 1: | Step 2: | Step 3: | Answer: | |
|---|---|---|---|---|---|
a. | Raise everything to the | Rewrite with positive exponents. | Create ones with common factors. Rewrite. | ||
b. | Raise everything to the | Rewrite with positive exponents. | Apply the exponent rules. |
Use the given information to write the explicit equation.