ࡱ> { vbjbjBrBr K$  ;:ZZ(((<<<<4p<r:EGGGGGG$8k(?kc"R(EE"ͻv10   (TkkYp Z z: Notes Geometric Sequences Arithmetic sequences _____________ a constant to get the next term (common ____________) 1, 4, 7, 10, 13, . 15, 11, 7, 3, . Geometric sequences - __________ a constant to get the next term 2, 4, 8, 16, 32, .. 9, -3, 1, -1/3, .. In a geometric sequence, the __________ of any term to the previous term is ______________. You keep ______________ by the SAME number to get the next number in the sequence. The same number is called the _____________ and is denoted by __________. Find r for the following sequences. Write a ratio  EMBED Equation.DSMT4  , then simplify. 1. 4, 8, 16, 32 2. 8, 24, 72, 216 3. 6, 2, 2/3, 2/9 4. 5, 10, 15, 20 Writing a rule for a geometric sequence:  EMBED Equation.DSMT4  r is the _________________, a1 is the ________________, n is the _________________ Example 1: Write a rule for the nth term of the sequence 6, 24, 96, 384, Then find a7. Example 2: Write a rule for the nth term of the sequence 1, 6, 36, 216, 1296, Then find a8. Now You Try: Write a rule for the nth term of the sequence  7, 14, 28, 56, 128, . . . Then find Writing a rule when youre not given the first term 1. Use the formula to find the first term. Plug in values for r, n, and anand solve for a1. 2. Write the rule for the nth term. Use the basic formula and plug in r, and a1. Example 3: If a3 = 18 and the common ratio is 3, write a rule for the nth term. Now You Try: If a4=8 and the common ratio is 2, write a rule for the nth term. Graphing the sequence 1. The domain is all positive integers (1,2, 3, 4, 5, ) 2. Plug in these values to find the y values 3. Plot the points and connect with a smooth curve. Example 4: Graph the sequence from the Example 3:  EMBED Equation.DSMT4  any term the previous term  EMBED Equation.DSMT4   ! " ' 9 D H x z ~     ! 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