Ch. 13 Review

13-1
This week I'm going to do a review on 13-1 where we learned about arithmetic and geometric sequences. We learned how to identify a sequence as arithmetic or geometric, how to find the nth term in a sequence, and how many terms are in a sequence. We also learned how to find the mean for both types of sequences.
-arithmetic sequence: sequence that is generated by adding the same number each time
  formula: tn = t1 + (n-1)d
-geometric sequence: sequence that is generated by multiplying the same number each time 
  formula: tn = t1 x r^(n-1)
-arithmetic mean: a + b/2
-geometric mean: square root of ab


Example 1: Identify the following as arithmetic or geometric and find the formula for the nth term.
4,8,16,32,...
-geometric
-tn = t1 x r^(n-1)
        4 x 2^(n-1)
        4 x 2^n x 2^-1
        4 x 2^n/2
        = 2 x 2^n


Example 2: Find the indicated term of the arithmetic sequence.
t1 = 3, t4 = 12, t30 = ?
- 3 + d + d + d = 12
  3 + 3d = 12
  3d = 9
   d = 3
-t30 = 3 + (30 - 1) (3)
 = 90