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Name: __________________________ Date: ________________Period: ___________Common Differences vs. Common Ratios Arithmetic Seqences:If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence. The number added to each term is constant (always the same). This is called a common difference. We use d to represent the common difference.To find the common difference, subtract the first term from the second term.For Example: 1, 4, 7, 10, 13, 16, ... has a common difference of d = 3Geometric Sequences:Geometric Sequence is a sequence?of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. We use r to indicate the common ratio.To find the common ratio, you divide the first time by the second term.For Example: The geometric series?3, 6, 12, 24, 48, . . .?has common ratio?r?= 2.For each of the following sequences. Find the common difference or common ratio. (Next to pattern write d = ___ or r = ___) Identify whether the sequence is Arithmetic or Geometric.-4, 0, 4, 8, 12, ...,? Pattern: __________Circle : Arithmetic / Geometric2.) 3, 9, 27, 81, … Pattern: __________Circle : Arithmetic / Geometric3.) 6, 11, 16, 21, … Pattern: __________Circle : Arithmetic / Geometric4.) 7, 4, 1, -2, … Pattern: __________Circle : Arithmetic / Geometric5.) 972, 324, 108, 36, … Pattern: __________Circle : Arithmetic / Geometric6.) 4, 5, 6.25, … Pattern: __________Circle : Arithmetic / Geometric7.) 4, -2.5, -9, … Pattern: __________Circle : Arithmetic / Geometric8.) 8, 17.6, 27.2, … Pattern: __________Circle : Arithmetic / Geometric9.) 864, -288, 96, … Pattern: __________Circle : Arithmetic / Geometric10.) 75, 100, 125, … Pattern: __________ Circle : Arithmetic / GeometricComplete the problems below.11.)Bounce363220-762000Height1242123612.) Tom’s bank balances at the end of months 1, 2, and 3 are $1600, $1664, and $1730.56. What will Tom’s balance be at the end of month 5? ____________13.) Consider the geometric sequence 6, ?18, 54…. Select all that apply.?A. The common ratio is 3.?B. The 6th term is ?1458. ?C. The 4th term is ?3 times 54.?D. 6(?3)11 is smaller than 6(?3)10.Find the indicated term by using the common ratio.14.) 108, ?72, 48, …; 5th term15.) Find the next three terms of the sequence 5, 15, 45, 135… ................
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