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Bellwork

Bellwork. Write the Explicit equation for a geometric sequence where a 1 =-2 and a 5 =-32 Write a Recursive formula for 4, 1, -2, -5, -8,…. Bellwork. Write the explicit expression for a geometric sequence where a 1 =-2 and a 5 =-32. or. Bellwork.

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Bellwork

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  1. Bellwork • Write the Explicit equation for a geometric sequence where a1=-2 and a5=-32 • Write a Recursive formula for 4, 1, -2, -5, -8,…

  2. Bellwork • Write the explicit expression for a geometric sequence where a1=-2 and a5=-32 or

  3. Bellwork Write a Recursive formula for 4, 1, -2, -5, -8,…

  4. End in Mind • Miranda arranges some rows of dominoes so that after she knocks over the first one, each domino knocks over two more dominoes when it falls. If there are ten rows, how many dominoes does Miranda use?

  5. Vocabulary and Formulas • Series- The result when the terms of a sequence are added together • The sum of the first n terms is denoted Sn and is called the partial sum Arithmetic Geometric or or

  6. The process… • Arithmetic or Geometric? • What am I given? • Which Formula do I use? Plug it all in!... If you don’t have enough information, use what you do know to find what you don’t.

  7. Example 1:Find the Partial sum of the Arithmetic Series Givens: The first term is 14 The 30th term is 101

  8. Which Formula? Find the Partial sum of the Arithmetic Series Arithmetic Do we know d? or No! S0…

  9. Plug in what we know and simplify Answer: The sum of the first 30 terms (the partial sum) of this sequence is 1,725.

  10. Example 2:Find the Partial sum of the Arithmetic Series Givens: The first term is 7 We are finding the sum of the first 10 terms The common difference is 8

  11. Which Formula? Find the Partial sum of the Arithmetic Series Arithmetic Do we know d? or Yes! S0…

  12. Plug in what we know and simplify Answer: The sum of the first 10 terms (the partial sum) of this sequence is 430.

  13. Example 3:Find the Partial sum of the Arithmetic Series Givens: The first term is 12 The last term of the ones we’re adding together is 180 The common difference is 7

  14. Which Formula? Find the Partial sum of the Arithmetic Series Arithmetic Do we know d? or Yes! S0…

  15. Plug in what we know and simplify Oh No! We don’t know n!!!

  16. Let’s Find n! Now we know n is 25, so we can go back and finish solving!

  17. Plug in what we know and simplify Oh No! We don’t know n!!! We found n! It’s 25! Answer: The partial sum is 2400

  18. Example 4:Find the Partial sum of the Geometric Series Givens: The first term is 16 The common ratio is 2 We are finding the sum of the first 8 terms

  19. Which Formula? Find the Partial sum of the Geometric Series Geometric Which Formula uses what we’re given??? or We’re given n, not an

  20. Plug in what we know and simplify Answer: The sum of the first 8 terms of the sequence (the partial sum) is 4,080

  21. Example 5:Find the Partial sum of the Geometric Series Givens: The first term is 1 The last term of the ones we’re adding together is 81 The common ratio is 3

  22. Which Formula? Find the Partial sum of the Geometric Series Geometric Which Formula uses what we’re given??? or We’re given an not n

  23. Plug in what we know and simplify Answer: The partial sum of the geometric sequence is 121.

  24. Partial Sum Practice: • Find the partial sum of the arithmetic sequence where a1=-3 and a8=32 • Find the partial sum of the geometric sequence where a1=2, an=2048, and r=4 • Find the partial sum of the arithmetic sequence 9, 14, 19, 24,…59 • Find the partial sum of the geometric sequence where a1=4, r=5, and n=6 • Find the partial sum of the arithmetic sequence where a1=15, n=10, and d=-2

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