Math 3 - Module 6 Honors Topics

Exponential and Logarithmic Inequalities Exponential inequality rules: Logarithmic inequality rules: If the bases of the exponential inequality are not the same, you must “log both side” to get the variable out of the exponent. **Always check solutions for logarithms- must have only positives after the log

Examples of Exponential and Logarithmic Inequalities Solve each inequality.

Non-Arithmetic and Non-Geometric Sequences & Series We studied arithmetic and geometric sequences and series, but there are some sequences and series that are neither arithmetic nor geometric. Sequences can be generated using any pattern of n, the location and number of each term. generates the following terms. A table is a good way to organize the terms. *This sequence does not have a common difference or common ratio n 1 2 3 4 5 6 -1 7 14 23 34

Terms of Sequences Find the first 4 terms of each sequence. *These are all explicit formulas, but can you use recursive? n 1 2 3 4 1/5 1/3 3/7 n 1 2 3 4 5 7 11 19

Examples of Recursive Formulas Find the first 4 terms of each sequence. Terms: -4, -7, -13, -25 Terms: 5, 7, 11, 19 Now that you generated terms, can you write the formulas? n 1 2 3 4 -4 -7 -13 -25 n 1 2 3 4 1/2 1/4 1/16 1/256

Write Explicit Formulas You may want to organize the terms in a table to compare the terms to the values of n. Do you add to n? Subtract? Multiply? Divide? Square it? Write the explicit formula for the apparent nth term of the sequence. 1, 4, 7, 10, 13, … Formula: 2, 5, 10, 17, 26 n 1 2 3 4 5 7 10 13 n 1 2 3 4 5 10 17 26

Sigma Notation Find the indicated sum.