Geometric Sequences Advanced Math Topics Mrs Mongold Reminder

Geometric Sequences Advanced Math Topics Mrs. Mongold

Reminder: Arithmetic Sequence Ø Definition: l l Sequence in which the difference between any term and the term before it is a constant. i. e. you are adding or subtracting the same number each time Ø Example: l l 2, 4, 6, 8, … You are adding 2 to each term to get the next 10, 9, 8, 7, … You are subtracting 1 from each term to get the next

Common Difference Ø Definition: l The value of an – an-1 Ø Example: l 2, 4, 6, 8, … l 4 – 2 = 2 6 – 4 = 2 8 – 6 = 2 l d= 2 l l

Geometric Sequence Ø Definition: l l Sequence in which the ratio of any term to the term before it is a constant. i. e. each term is multiplied or divided by the same number Ø Example: l l 2, 4, 8, 16, … You multiply the previous term by 2 to get the next number 81, 27, 9, 3, … You divide each term by 3 to get the next number

Common Ratio Ø The value of an divided by an-1 Ø Example: l 2, 4, 8, 16, … 4/2 = 2 8/4 = 2 16/8 = 2 l So common ratio r =2 l l If the pattern is dividing the common ratio is a fraction!!!

Geometric Sequence 0. 05, 0. 25, 1. 25, 6. 25, … Ø Explicit Formula l l an=a 1 rn-1 Pattern is previous term times 5 so r = 5 an=a 1 rn-1 an=. 05 (5)n-1 Ø Recursive Formula l l l an=(an-1)r Pattern is previous term times 5 so r = 5 an=(an-1)r an =(an-1)5 an=5(an-1)

Examples l 1, -5, 25, -125, … l -4, -8/3, -16/9, -32/27…

More Examples Ø a 1 = 4, r=3

More Examples Ø a 1 = 8, r= ½

More Examples Ø a 1 = 25, r= -5

More Examples Ø

More Examples Ø 100, 20, 4, 0. 8, …

More Examples Ø 1, 3, 6, 10, …

More Examples Ø 12, 17, 22, 27, …

More Examples Ø 0, 1, -1, 0, 1, -1 …

More Examples Ø 25, 22, 19, 16, …

More Examples Ø

Homework Ø Arithmetic Sequences HW #2 Ø Geometric Sequences HW #3