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Homework Review

Homework Review. GPS Geometry Day 72 (11-20-13). UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3. Geometric Sequences. Geometric Sequences.

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Homework Review

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  1. Homework Review

  2. GPS GeometryDay 72 (11-20-13) UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3

  3. Geometric Sequences

  4. Geometric Sequences • In geometric sequences, you multiply by a common ratio each time. • 1, 2, 4, 8, 16, ... multiply by 2 • 27, 9, 3, 1, 1/3, ...Divide by 3 which means multiply by 1/3

  5. Geometric Sequences • Find the 8th term of the sequence: 2,6,18,… Determine the pattern: Multiply by 3 (known as the common ratio) Write the new sequence: 2,6,18,54,162,486,1458,4374 So the 8th term is 4374.

  6. Geometric Sequences • Again, use a formula to find large numbers. • an = a1 • (r)n-1 • an = The term you want • a1 = The first term • r = The common ration • n = The number of the term you want

  7. Geometric Sequences • Find the 10th term of the sequence : 4,8,16,… an = a1 • (r)n-1 • a1 = 4 • r = 2 • n = 10

  8. Geometric Sequences an = a1 • (r)n-1 a10 = 4 • (2)10-1 a10 = 4• (2)9 a10 = 4• 512 a10 = 2048

  9. Geometric Sequences • Find the 6th term of the sequence : 8,-4,2 ,… an = a1 • (r)n-1 • a1 = 8 • r = ??? • n = 6

  10. Geometric Sequences • Find the ninth term of a sequence if a3 = 63 and r = -3 a1= ? n= 9 r = -3 a9 = ? There are 2 unknowns so you must…

  11. Geometric Sequences • First find a1. • Use the sequences formula substituting a3 in for an.  a3 = 63 • a3 = a1 • (-3)3-1 • 63 = a1 • (-3)2 • 63= a1 • 9 • 7 = a1

  12. Geometric Sequences • Now that you know t1, substitute again to find tn. an = a1 • (r)n-1 a9 = 7• (-3)9-1 a9 = 7• (-3)8 a9 = 7• 6561 a9 = 45927

  13. Geometric Sequences • Find the eighth term of a sequence if a2 = 2 and a6 = 512

  14. Application A 5-day rain caused the Olentagy River to rise. After the first day, the river rose one inch. Each day the rise in the river tripled. How much has the river risen after 5 days?

  15. Class work Coach Book Page 93 and 94

  16. Homework Page 145 #1-17 (odd), skip graph on 7 & 9

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