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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:number of steps. With the use of such recursions the values of even the most complicated functions used in number theory can be calculated in a finite number
The Latin technical term "recursion" refers to a certain kind of stepping backwards in the sequence of natural numbers, which necessarily ends after a finite
In her book Recursive Functions in Computer Theory, Péter describes the important connections between recursion and computer lanquages.
1
of 5
Page
.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.
i. u, - 20
Un = Un-1 +6 where n 22
il. u = 47
U, = Un-1 -3 where n22
b. Start with 47. Keep subtracting 3.
iii. u, = 32
u, = 1.5 - un-1 where n22
c. Start with 20. Keep adding 6.
iv, u = -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. @
3.
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
Hunevise mathematician Rózsa Péter (1905-1977) was the first person to propose the study of fecursion in its own right. In an interview she described recursion
in this way:
of steps.
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