Question

mathlab please copy and paste the code and output

Q1. (50 points) Consider the following mathematical sequence for any mumber fathe sequence, the first number is 1 = 0. The remaining terms are computed via the following method. The second number of the sequence is given by 1 /2 f iseve Ty - 3x + 1 if, is add The third number of the sequence is given by 1 /2 fils even 133ry + 1 ifr, is odd Thus, the nth number of the sequence is given by 1-1/2 if is even In=3,- 1 + 1 f 1-1 is odd Thus, for I = 9, the sequence is 9,28, 14.7.22, 11.34, 17,52, 26, 13, 40,20, 10,5, 16, 8, 4.2.1 (a) Create a MATLAB function called sequencel that returns the above sequence up to 10 terms. Your function should have a single input argumenta, and it should retum a vector containing the sequence up to 10 terms, ie. the output of the function should be a vector containing the terms 21.12.17...... ) Use a for or while loop for this function Display and execute this function on a live script with a value of a = 27 (b) The above sequence, if run long enough, will eventually end up with a term equaling 1 Modify the above function by creating a new function sequence that returns the above sequence up to the point it hits the first time. Thus, the output of the function should be vector containing the terms . ...... 1). Use a while loop for this function. Display and execute this function on a live script with a value of a = 19. (c) (BONUS 10p) Modify the function in (b) to create a new function sequence that returns the mumber of terms in the sequence before it hits 1. Thus, is the number of terms in the output vector of part (b). Call this function from a live script for a range of values from a = 1 to - 100, and store the values returned by the function in a vector S. Store the values I to 100 in a vector A. Plot S versus A. Le A along the X-axis, and Salong they 8

Answer 1

Below are the code in MATLAB for the above question:

************************************ 1(a) ************************************
% function sequence1 to find sequence
% upto 10 terms.
function x = sequence1(a)
% assigning x(0) to a.
x = a;
% now finding upto 10 terms using
% given condition.
for i = 2:10
% if previous element is even
if(mod(x(i-1),2)==0)
x(i) = x(i-1)/2;
% if previous element is odd
else
x(i) = 3*x(i-1)+1;
end
end
end

************************************ 1(b) ************************************
function x = sequence2(a)
% assigning x(0) to a.
x = a;
% now finding ten terms using
% given terms.
i = 2;
while(1)
% first cheking if previous element is
% 1 or not
if(x(i-1)==1)
break;
end
  
% if previous element is even
if(mod(x(i-1),2)==0)
x(i) = x(i-1)/2;
% if previous element is odd
else
x(i) = 3*x(i-1)+1;
end
i = i + 1;
end
end

************************************ 1(c) ************************************
function s = sequence3(a)
% assigning x(0) to a.
x = a;
% now finding ten terms using
% given terms.
i = 2;
% finding element of sequence
while(1)
% first cheking if previous element is
% 1 or not
if(x(i-1)==1)
break;
end
  
% if previous element is even
if(mod(x(i-1),2)==0)
x(i) = x(i-1)/2;
% if previous element is odd
else
x(i) = 3*x(i-1)+1;
end
i = i + 1;
end
% storing size of vector x before it hits 1.
s = length(x)-1;
end

CODES IN LIVESCRIPT:

% test for 1(a)
sequence1(27)

% test for 1(b)
sequence2(19)

% test for 1(c)
S = zeros(1,100);
A = zeros(1,100);
% loop to find sequence length
% range from 1 to 100.
for i = 1:100
% storing i to A
A(i) = i;
% storing length of sequence
% before it hits 1 to vector S.
S(i) = sequence3(i);
end
% plotting A vs S.
plot(A,S);

Refer to the screenshot attached below to better understand the code and indentation:

************************************ 1(a) ************************************

function sequencel to find sequence $upto 10 terms. function x = sequencel (a) $ assigning x(0) to a. - 56GBEE coonWN II $now finding upto 10 terms using given condition. for i = 2:10 if previous element is even if (mod (x(i-1),2)==0) x(i) = x(i-1)/2; $ if previous element is odd else x(i) = 3*x(i-1)+1; end end end


************************************ 1(b) ************************************

function x = sequence2 (a) assigning x(0) to a. x = a; now finding ten terms using $ given terms. i = 2; while (1) first cheking if previous element is $1 or not if(x(i-1)==1) break; end $ if previous element is even if (mod (x(i-1),2)==0) x(i) = x(i-1)/2; $if previous element is odd else x(i) = 3*x(i-1)+1; end i = i + 1; end


************************************ 1(c) ************************************

function s = sequence3 (a) assigning x(0) to a. I now finding ten terms using $ given terms. i = 2; finding element of sequence while (1) first cheking if previous element is $1 or not if(x(i-1)==1) break; end TILLITI TI $ if previous element is even if (mod (x(i-1),2)==0) x(i) = x(i-1)/2; $ if previous element is odd else x(i) = 3**(1-1)+1; end i = i + 1; end storing size of vector x before it hits i. s = length(x)-1;


Output:


sequencel(27) ans = 1x10 double 27 82 41 124 62 31 94 47 142 71 sequence2 (19) ans = 1x21 double 1958 2988 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1



S = zeros(1,100); A = zeros(1,100); % loop to find sequence length % range from 1 to 100. for i = 1:100 % storing i to A A(i) = i; % storing length of sequence % before it hits 1 to vector S. S(i) = sequence3(i); end % plotting A vs S. plot(A,S);


о o 10 20 30 40 50 60 70 80 90 100


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