Warm Up Find the next 3 terms in the following sequence and describe the pattern 1) 3, 7, 11,15, 19, ___, _, _ Pattern:_____________.

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Presentation transcript:

Warm Up Find the next 3 terms in the following sequence and describe the pattern 1) 3, 7, 11,15, 19, _______, _______, _______ Pattern:_________________ 2) -3, -1, 1,3, 5, _______, _______, _______ Pattern:_________________ 3) 2, 6, 18, 54, 162, _______, _______, _______ Pattern:_________________

Today’s Lesson: Geometric Sequences March 3, 2014

Recall……… Problems number 1 and 2 are different from number 3 because the terms increase by adding a certain amount. #1 and #2 are called arithmetic sequences #3 increased by a factor of 3. Arithmetic sequences did not increase by being multiplied by a number. In fact #3 is actually a geometric sequence.

Geometric Sequences Geometric Sequence: a sequence in which each term after the first is found by multiplying the previous term by a constant value called the common ratio.

Think about it… What if your pay check started at $100 a week and doubled every week. What would your salary be after four weeks?

Geometric Sequence Starting $100. After one week - $200 After two weeks - $400 After three weeks - $800 After four weeks - $1600. These values form a geometric sequence.

Still Don’t Get It? Find the first five terms of the geometric sequence with a1 = -3 and common ratio (r) of 5. ANSWER: -3, -15, -75, -375, -1875

Geometric Sequence Find the common ratio of the sequence 2, -4, 8, -16, 32, … To find the common ratio, divide any term by the previous term. 8 ÷ -4 = -2 r = -2

Geometric Sequence Let’s figure out the formula(s)… Recursive form: NEXT = ____ NOW OR an=an-1•r Explicit form: =(y = abx )

Salary Example Starting $100. After one week - $200 After two weeks - $400 After three weeks - $800 After four weeks - $1600. Recursive form: NEXT = ____ NOW Explicit form: an = a1•rn-1

Example an = a1•rn-1 Find the 10th term of the geometric sequence with a1 = 2000 and a common ratio of 1/2.

Example an = a1•rn-1 Find the next two terms in the sequence -64, -16, -4 ...

Classwork

Classwork

Classwork

Geometric Sequences Worksheet: Evens Only Homework Geometric Sequences Worksheet: Evens Only