**Do Now** • Determine the constant difference and the explicit formula of arithmetic sequence of 1, 5, 9, 13… • Determine the implicit formula of • Find the values of a and d if we know that a10 = 38 and a15 = 18. 1.6: Geometric Sequences

**Worksheet Key** 1.6: Geometric Sequences

**Geometric Sequences** section 12.3 1.6: Geometric Sequences

**Definitions** • A geometric sequence is a list of numbers that have a COMMON RATIO (r) meaning you DIVIDED by the same number. • To find r = DIVIDE THE SECOND NUMBER TO THE FIRST NUMBER 1.6: Geometric Sequences

**Is it Geometric?** Determine whether these sequences are geometric. If it is, determine the ratio. • {1, 3, 9, 27, 81...} • {180, 90, 0, –90, –180...} • {5, 1, 0.2, 0.04, 0.008...} • {–50, –32, –18, –8, –2...} YES r = 3 Arithmetic YES r = 0.2 NO 1.6: Geometric Sequences

**Formulas** Explicit Formula: Recursive Formula: 1.6: Geometric Sequences

**Steps** • Find the common ratio • Use the formula and determine the rule • Evaluate for the missing variable • Check 1.6: Geometric Sequences

**Example 1** Find the 6th term and explicit rule for given, a1 = 5, r = 2 Step 1: Find the common ratio. 1.6: Geometric Sequences

**Example 1** Find the 6th term and explicit rule for given, a1 = 5, r = 2 Step 2: Use the formula and determine the term 1.6: Geometric Sequences

**Example 1** Find the 6th term and explicit rule for given, a1 = 5, r = 2 Step 3: Evaluate for the missing variable 1.6: Geometric Sequences

**Example 1** Find the 6th term and explicit rule for given, a1 = 5, r = 2 Step 4: Check 1.6: Geometric Sequences

**Example 2** Find the 10th term and explicit rule for the following geometric sequence of 16, –8, 4, –2,… 1.6: Geometric Sequences

**Your Turn** Find the 5th term and explicit rule for given a1 = 1/6, a2 = –1/18. Leave answers in fraction form. 1.6: Geometric Sequences

**Example 3** Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324. Step 1: Find the common ratio. 1.6: Geometric Sequences

**Example 3** Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324. Step 2: Find a1. Consider both the positive and negative values for r. or 1.6: Geometric Sequences

**Example 3** Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324. Step 3: Write the rule and evaluate for a8. Consider both the positive and negative values for r. or 1.6: Geometric Sequences

**Example 4** Find the 8th term of the geometric sequence with a2 = 80 and a4 = 1280 1.6: Geometric Sequences

**Your Turn** Find the 8th term of the geometric sequence and its implicit formula with a3 = 108 and a5 = 3888 1.6: Geometric Sequences

**Assignment** Geometric Sequences Worksheet 1.6: Geometric Sequences