1 / 8

11.3 – Geometric Sequences

11.3 – Geometric Sequences. What is a Geometric Sequence?. In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio . Unlike in an arithmetic sequence, the difference between consecutive terms varies.

bell-lane
Download Presentation

11.3 – Geometric Sequences

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11.3 – Geometric Sequences

  2. What is a Geometric Sequence? • In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio. • Unlike in an arithmetic sequence, the difference between consecutive terms varies. • We look for multiplication to identify geometric sequences.

  3. Ex: Determine if the sequence is geometric. If so, identify the common ratio • 1, -6, 36, -216 yes. Common ratio=-6 • 2, 4, 6, 8 no. No common ratio

  4. Important Formulas for Geometric Sequence: • Recursive Formula • Explicit Formula an = (an– 1 ) r an = a1 * r n-1 Where: an is the nth term in the sequence a1 is the first term n is the number of the term r is the common ratio • Geometric Mean Find the product of the two values and then take the square root of the answer.

  5. Let’s start with the geometric mean • Find the geometric mean between 3 and 48 Let’s try one: Find the geometric mean between 28 and 5103

  6. Ex: Write the explicit formula for each sequence First term: a1 = 7 Common ratio = 1/3 Explicit: an = a1 * r n-1 a1 = 7(1/3) (1-1) = 7 a2 = 7(1/3) (2-1) = 7/3 a3 = 7(1/3) (3-1) = 7/9 a4 = 7(1/3) (4-1) = 7/27 a5 = 7(1/3) (5-1) = 7/81 Now find the first five terms:

  7. Explicit Arithmetic Sequence Problem Find the 19th term in the sequence of 11,33,99,297 . . . an = a1 * r n-1 Start with the explicit sequence formula Find the common ratio between the values. Common ratio = 3 a19 = 11 (3) (19-1) Plug in known values a19 = 11(3)18 =4,261,626,379 Simplify

  8. Let’s try one Find the 10th term in the sequence of 1, -6, 36, -216 . . . an = a1 * r n-1 Start with the explicit sequence formula Find the common ratio between the values. Common ratio = -6 a10 = 1 (-6) (10-1) Plug in known values a10 = 1(-6)9 = -10,077,696 Simplify

More Related