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ALGEBRA U7 2015-16 HW 7-1 ARITHMETIC/GEOMETRIC SEQUENCES For problems 1-5: a) Write the next two terms in the sequence b) Identify the sequence as arithmetic, geometric, or neither, AND why? 1) 27, 31, 35, … a) _______________ b) __________________________________________ 2) 58, 45, 32, … a) _______________ b) __________________________________________ 3) 1, 4, 9, 16, 25, … a) _______________ b) __________________________________________ 4) 3, 9, 27, 81, … a) _______________ b) __________________________________________ a) _______________ b) __________________________________________ Challenge: 5) 27, 36, 48, … 6. Complete the table and answer the questions below: a) What type of function is this? Why? b) What type of sequence is represented? c) Write an equation for the function represented in the table. n f(n) 0 1 3 2 6 3 9 4 12 7. Complete the table and answer the questions below: a) What type of function is this? Why? b) What type of sequence is represented? n f(n) 0 6 1 12 2 24 3 48 c) Write an equation for the function represented in the table. 8. Given the function f(n ) 4 n 1, find f(3): 9. Given the formula an = 4n – 1, find the following: a) a3 b) a0 c) a-2 10. Describe the rate of change (Positive or Negative) and give its value for each table below.: 11. Solve the following system: 5x 3y 4 3 x 2y 9 ALGEBRA U7 2015-16 HW 7 - 2 EXPLICIT VS RECURSIVE Identify the following as either an explicit or a recursive formula. Find the first four terms of each sequence. 1) 3) 5) an 3 n 2) a1 1 4) an 2an1 5 Given the sequence: an n 2 n a1 2 an1 4an 1 2, 7, 12, 17, 22,… a) List the next three terms of the sequence. b) Write an explicit formula for an. c) Write a recursive definition for the sequence. 6) 7) Which of the following is an equation that has a zero slope and goes through the point (3, -5)? (1) x = 3 (3) y = -5 (2) x = -5 (4) y = 3 Tina wants to make a rectangular sandbox that has a perimeter of 78 inches . The width is three more than twice the length. Determine the dimensions of the sandbox. 8) Graph a line that has a slope of 2 and goes through the point (-6, 1). 3 Write the equation of the line graphed. 9) Which equation below represents an exponential function? (1) 4 x 2 3 19 (3) 3x 7 25 (2) 5 x 125 (4) 12 2x 5 ALGEBRA 1 1. 2015-16 SEQUENCES FORMULAS Write the first five terms of each sequence. a) an = 12 – 3n b) a1 = 1 an = 2an-1 +1 For each of the following sequences in #2 and 3, determine the following: a. b. c. d. 2. What type of sequence is it and why? Write an explicit formula for the sequence. Write a recursive formula for the sequence. Find the 12th term of the sequence. 17, 23, 29, 35 … 3. –.125, .5, –2, 8 … HW 7-3 4. Consider the arithmetic sequence 13, 24, 35 … a. Find an explicit formula for the sequence in terms of n. b. Find the 40th term. c. If the nth term is 299, find the value of n. 5. 6. Leslie noticed that the daily number of text messages she received over the course of two months form an arithmetic sequence. If she received 6 texts on the first day of the two months and received an additional 3 more texts each following day, how many texts did she receive on: a) day 27? b) day 60? Justin Bieber’s dad bought a baseball card 20 years ago for $0.50. He found out recently that it has been appreciating in value at a rate of 22% annually. If he were to sell the card today, how much would it be worth?