In her book Recursive Functions in Computer Theory, Péter describes the important connections between recursion and comnuter lui Exercises Practice Your Skills 1. Match each description of a sequence to its recursive formula. a. The first term is -18. Keep adding 4.3. iu = 20 Un = Un-1 +6 where n22 il. u = 47 4, = Un-1 -3 where n22 b. Start with 47. Keep subtracting 3. ii. u, =32 u, = 1.5 - un-1 c. Start with 20. Keep adding 6. where n22 İV, Uj =-18 u, = Un-1+ 4.3 where n > 2 d. The first term is 32. Keep multiplying by 1.5. 2. For each sequence in Exercise 1, write the first 4 terms of the sequence and identify it as arithmetic or geometric. State the common difference or the common ratio for each sequence. @ 3. Write a recursive formula and use it to find the missing table values. @ 4 5 40 36.55 33.1 29.65 12.4 ... 4. Write a recursive formula to generate an arithmetic sequence with a first term 6 and a common difference 3.2. Find the 10th term. 5. Write a recursive formula to generate each sequence. Then find the indicated term. a. 2, 6, 10, 14,... Find the 15th term. b. 0.4, 0.04, 0.004, 0.0004, ... Find the 10th term. c. -2, -8, -14, -20, -26, ... Find the 30th term. d. -6.24, -4.03, -1.82, 0.39, ... Find the 20th term. @ History CONNECTION Hungarian mathematician Rózsa Péter (1905–1977) was the first person to propose the stuby of fecursion in its own right. In an interview she described recursion in this way: ura trboicalterm"recursion" refers to a certain kind of stepping backwaras in the sequence of natural numbers, which necessarily ends after a finite me rof stens With the use of such recursions the values of even the most complicated functions used in number theory can be calgulated in a finite number of steps.