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Math 130 Spring 2017 Homework #1 1. Consider the visual pattern in the progression below: (a) Explain how the sequence 1, 3, 5, 7, … relates to the pictures. (b) Explain how the sequence 4, 10, 16, 22, … relates to the pictures. (c) Identify another number sequence related to the picture and explain what the relationship is. 2. Use the rule to complete the data table. (a) The next term in the sequence is the preceding term multiplied by 10. The starting term is 5. n 0 1 2 3 4 5 A(n) (b) Each term in the sequence is found by subtracting 4 from the position number. Start with position 0. n 0 1 2 3 4 5 B(n) (c) The starting term is 1. Each remaining terms is the product of the position number and the preceding term. n 0 1 2 3 4 5 C(n) 1 Math 130 Spring 2017 3. Fill in the table showing the position numbers and terms, and then find a pattern in the sequence. Use the pattern to write the rule in “short-hand notation”. (There may be more than one rule possible.) (a) 1, 2, 4, 8, 16, . . . n a(n) (b) 1, 4, 9, 16, 25, 36, . . . n b(n) (c) 1, ½, ⅓, ¼, ⅕, . . . n c(n) (d) 0, ½, ⅔, ¾, ⅘, ⅚, . . . n d(n) 4. Find the pattern and use it to write the next two equations. Then complete the sequence table. (a) A(0) = 17 A(3) = A(2) – 4 n A(n) A(1) = A(0) – 4 A(4) = A(2) = A(1) – 4 A(5) = 0 1 2 3 4 5 6 7 2 Math 130 (b) Spring 2017 B(0) = 0×1 + 5 B(3) = 3×4 + 5 B(1) = 1×2 + 5 B(2) = 2×3 + 54 n B(n) 0 1 2 3 4 5 6 7 5. The National Weather Service recorded the following average temperatures (in ℉) for Central Park in NYC in May 2014. Use the notation T(n) to stand for the temperature n days after April 30. Day April 30 May 1 May 2 May 3 May 4 May 5 May 6 n Temperature (℉) 65 63 63 60 60 62 (a) Fill in the row of positions (labeled “n”). (b) Fill in the blanks to explain the meaning of T(0): T(0) is the (in Central Park) on . (c) What is the numerical value of T(1)? (d) What is the numerical value of T(4)? (e) The average temperature for May 25 was 68℉. Express this using the T(n) notation. In other words, T( )= . (f) Give a verbal statement explaining the equation T(33) = 70 in terms of a date, temperature, and the context given here. 3