4. A good example of a combination of geometric and arithmetic sequences is the musical scale: C, C*, D, D*, E, F, F*, G, G*, A, A*, B, C. The frequency of an octave above one note is just twice the frequency. For example: theoretically the first C is 2 hz. The second octave C is 2(2) = 4 Hz. The nth octave is 2(2)"- Hz. The frequency of one note to the next is just a factor of 2 " . So for 1+ example the first C* is 2(2 ") = 2 . The first D is 2(2") = 2 a. Find the sequence that corresponds to the frequency of the ath octave of A. [2 marks] b. In practice musicians generally tune their instruments to A = 440 Hz. If this is supposed to be the 8th octave, how far off is this from the theoretical value? [2 marks] Part D: Communication 17 Read the questions and answer them in the space provided. The questions require mathematical calculations; please show all of your work. 1. a) Write the last two terms of the series 81 + 324 + 486 + _+_[2 marks] b) Without adding explain how to find the sum of this series [2 marks]1. The grass on a golf course needs cut when it is 3 cm. If the height cf the grass is 15 mm on Sunday and it grcws at a rate of 3 mm per day, when is the next day it should he cut? [3 marks] 2. The 3rd term of an arithmetic sequence is 7, and the 7th term is 23. What is the rst term? [2 marks] 3. The 8111 term of an arithmetie sequence is 3 and the 100th term is 49. What is the recursive formula for the sequence? [3 marks] 4. What is the largest integer cf the farm 5:: + 7 that is less than 265'? [2 marks] 1. To insure he never eats the whole cake, Bobby only decides to eat half of what's left for each 2 serving. If E of the cake are left initially, and no one else but Bobby eats the cake, how big will Bobby's portion of the cake he on his 4th serving? [3 marks] I. The interior angles of an equilateral triangle are 60\". The interior angles of a square are 9t)\". The interior angles of a regular pentagon are lS". Determine the creature of interior angles of a regular n-gon (polygon with 1: equal sides and angles}. [3 marks] 3. [3 marks] The triangular nurnhers are the numbers in the scouence: l, 3, 6, It}, 15, a. Detennine the next three triangular numbers I). Find the recursive formula for the sequence c. Find the General form for the sequence 2. You are given two arithmetic sequences, one defined by the general term as, t,, = a + (n - 1)d, and the other defined by a discrete linear function, f(n) = cn + b. Under what conditions are the two sequences the same? [3 marks]