1. Lesson 7-7 Geometric Sequences

2.  Remember, an arithmetic sequence changes by adding (or subtracting) a constant to each term.  Ex: -4, 1, 6, 11, 16, …  Ex1 : Find the next three terms in the arithmetic sequence. -22, -15, -8, … +5 -1, 6, 13

3.  A geometric sequence changes by multiplying by a constant.  Ex: -4, -20, -100, -500, …  Ex2 : Find the next three terms in the arithmetic sequence. 4, -12, 36, … x 5 -108, 324, -972

4.  You can tell a sequence is geometric by: 1. Finding its constant factor, or 2. Check that the ratio of terms stays constant.  Ex3: -4, -20, -100, -500, …

5.  Ex 4: Determine whether the sequence is arithmetic, geometric or neither. 2, 8, 40, 80, …  Arithmetic – look for constant addend. 2, 8, 40, 80, … +6+32+40 Not arithmetic, there is no common addend

6.  Geometric – look for constant ratios. 2, 8, 40, 80, … Not geometric, there is no constant ratio Not arithmetic or geometric, so it must be neither

7.  Ex 5: Complete the table for the geometric sequence that starts at -10 and has a common factor (or ratio) of 2. Ex 6: Find the 8 th term in the sequence. TermExpansionValue 1-10 2-20 3-40 4 5 -80 -160 -1,280

8.  Looking at the expansion column of the table, what pattern do you see? This leads to a generic equation we can use to find any term of this sequence. TermExpansionValue 1-10 2-20 3-40 4 5 -80 -160