1 ;; The first three lines of this file were inserted by DrScheme. They record metadata
2 ;; about the language level of this file in a form that our tools can easily process.
3 #reader(lib "htdp-intermediate-reader.ss" "lang")((modname |23.2|) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
4 ;a-fives : N[>=0] -> number
5 ;Given n, determine recursively the value of the n-th term in the series 8, 13, 18, etc. where the first term has an index 0.
6 
7 (define (a-fives n)
8   (cond
9     [(zero? n) 8]
10     [else (+ 5 (a-fives (sub1 n)))]))
11 
12 ;a-fives-closed : N[>=0] -> number
13 ;A non-recursive function for finding the n-th term of the series 8, 13, 18, etc., where the first term has an index 0.
14 
15 (define (a-fives-closed n)
16   (+ (* n 5) 8))
17 
18 ;series : (N[>=0] -> number) N[>=0] -> number
19 ;Given a-term and n, determine the sum of the first n-th terms in the sequence a-term.
20 
21 (define (series a-term n)
22   (cond
23     [(zero? n) (a-term n)]
24     [else (+ (a-term n)
25              (series a-term (sub1 n)))]))
26 
27 ;sequence : (N -> number) N -> (listof number)
28 ;Given a-term and n, generate the sequence of the first nth terms in a-term as a (listof numbers).
29 
30 (define (sequence a-term n)
31   (build-list n a-term))
32 
33 (define (seq-a-fives n)
34   (sequence a-fives-closed n))
35 
36 ;arithmetic-term : N number -> (N -> number)
37 ;Given start and s (summand), return a function that consumes a natural number n and returns the nth-term in the arithmetic sequence.
38 (define (arithmetic-term start s)
39   (local ((define (a-term n)
40             (+ (* n s) start)))
41     a-term))
42 
43 (define a-fives2 (arithmetic-term 8 5))
44 (define evens (arithmetic-term 0 2))
45 
46 ;g-fives : N -> number
47 ;Recursively returns the nth term of the geometric sequence: 3, 15, 75, 275, ...
48 (define (g-fives n)
49   (cond
50     [(zero? n) 3]
51     [else (* 5 (g-fives (sub1 n)))]))
52 
53 ;g-fives-closed : N -> number
54 ;Non-recursively returns the nth term of the geometric sequence: 3, 15, 75, 275, ...
55 (define (g-fives-closed n)
56   (* (expt 5 n) 3))
57 
58 ;seq-g-fives : N -> (listof numbers)
59 ;Given n, returns a list of the first n-th terms in the g-fives sequence.
60 
61 (define (seq-g-fives n)
62   (build-list n g-fives-closed))
63 
64 ;geometric-series : number number -> (N -> number)
65 ;Given start and s, returns a function who computes the n-th term (where n is a natural number) of the geometric series with first term start with ratio s.
66 
67 (define (geometric-series start s)
68   (local ((define (g-term n)
69             (* (expt s n) start)))
70     g-term))
71 
72 (define g-fives2 (geometric-series 3 5))