1 / 10

Understanding Finite Differences in Sequences for Mathematical Induction

Explore how to find formulas for general terms using finite differences in sequences. Learn to identify linear, quadratic, and cubic patterns and apply them to solve for unknown constants. Practice with examples to master the concept.

dmorrison
Download Presentation

Understanding Finite Differences in Sequences for Mathematical Induction

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. Mathematical induction 9.4

  2. Finite differences • When given a sequence that is neither arithmetic nor geometric, we can try to find finite differences. • For example: • 2, 5, 10, 18, 30, 47, 70,…

  3. Finite differences • If the first difference is constant, our terms are linear (an arithmetic sequence) • If the second difference is constant, our formula for general terms is quadratic • If the third difference is constant, our formula for general terms is cubic. • Generalize the formula, plug in known values, and solve the system for the unknown constants.

  4. Example • Find a formula for the nth term • 3, 5, 8, 12, 17, 23, …

  5. Example continued

  6. Example • Find • 1, 7, 15, 25, 37, 51, …

  7. Example Continued

  8. Sums of powers

  9. Find the sum

  10. Homework • Pg642 #45-59 odd

More Related