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Daily Check

Daily Check. Find the first 3 terms of the following sequence: Write the formula for the following arithmetic sequence. -2, 1, 4, 7, 10. Math II. UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question:

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Daily Check

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  1. Daily Check • Find the first 3 terms of the following sequence: • Write the formula for the following arithmetic sequence. • -2, 1, 4, 7, 10

  2. Math II 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: MM2A3f,g

  3. Sequences and Series

  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

  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 ninth term of a sequence if a3 = 63 and r = -3 a1= ? n= 9 r = -3 a9 = ? There are 2 unknowns so you must…

  10. Geometric Sequences • First find t1. • Use the sequences formula substituting t3 in for tn.  a3 = 63 • a3 = a1 • (-3)3-1 • 63 = a1 • (-3)2 • 63= a1 • 9 • 7 = a1

  11. 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

  12. Class work Day 1: Workbook p. 159 #1-9, 13-15, 19 odd Day 2: Workbook p. 159 #2-8, 14, 20

  13. Homework Page 145 #2-16 (even)

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