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Sequences!

Sequences!. A PowerPoint Presentation just for you!. By the ever electrifying…. Pete Bokma and Randal Reiman. I’m a horse!. I’ll be your guide for this wonderful journey through the amazing world of sequences! I’m so happy, I can hardly contain myself!!!. Arithmetic.

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Sequences!

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  1. Sequences! A PowerPoint Presentation just for you! By the ever electrifying… Pete Bokma and Randal Reiman

  2. I’m a horse! I’ll be your guide for this wonderful journey through the amazing world of sequences! I’m so happy, I can hardly contain myself!!!

  3. Arithmetic • Here’s an arithmetic sequence that all my horse friends love… • -20, -10, 0, 10, 20, 30, 40… • My friend, Sugarface, figured out a closed-form solution for it… • T = -20 + (n – 1) x 10 • Pretty cool, right? Well with that solution we can figure out the 50th term… n • T = -20 + (50 – 1) x 10 470 50

  4. Arithmetic Part Deux • If you thought this excitement was over, you were sorely mistaken… • Let’s create a formula for the sum of n terms… • S = .5(10)n + [-20 - .5(10)] x n • Ok, once again, this is getting ridiculously exciting… • Let’s use our formula for DUM DUM DUM the sum of 25 terms… • S = 2 n .5(10)(25) + [-20 - .5(10)] x 25 2500 2 25

  5. Geometric rocks my socks • Yo, check it… • 2, 6, 18, 54, 162, 486, 1458… • closed-form in the heazy… • T = 2 (3) • 50th term anyone? n - 1 n • T = 4.79 E 23 2 (3) 50 - 1 50

  6. Geometric = NOT DONE YET • More intense sequences from me… Mr. Horse • a formula for the sum of n terms… • S = • muhahahahahahahaha • the sum of 25 terms… • S = 2 (1 – 3 ) 1 – 3 ______ n n ______ 2 (1 – 3 ) 1 – 3 25 8.47 E 11 25

  7. I am STILL a horse!

  8. Mixed • Now this is what I call a mixed sequence… • 0, 1, 5, 12, 22, 35, 51… • CLOSED-FORM SOLUTION!!!  • T = 1.5n - 3.5n + 2 • YEEEEEE-HA!!!!! It’s time to find that crazy 50th term… 2 n • T = 1.5(50) - 3.5(50) + 2 3577 2 50

  9. That was a hoot! THE END! We really must do it again sometime…

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