Question

106/); [15] A particular sequence has the recursive formula In+3 = In+1 +sin(tn) where n = 0,1,2,3,... and we have that to = 3.t1 = 1. Use a loop to calculate the first 10000 terms of the sequence. Then display these term values as red circles on a graph. The figure must have a title and axes labels. A table, with headings, must then be created with the first column showing the value of n (no decimals) and the 2 column the values tn rounded to 7 decimal places, BUT of the 10000 terms only display in the table the first 10 and the last 200 terms. This table must be displayed in the Command Window and additionally it must be written to a Microsoft Word (.doc) file.

Please use Matlab and good commenting.

Answer 1

Matlab code for the problem

clc; clear; % clearing the command window and workspace

t = zeros(1,10000); % initilizing the t vector with all zeros

t(1) = 3; % t_0 value

t(2) = 1; % t_1 value

for n = 1:1000-2 % loop to calculate first 10000 terms

t(n+2) = t(n+1) + sin(t(n)); % calculating 10000 terms of the sequence

end

plot(t,'ro'); % plotting the t values as red circles

title('t_{n+2} = t_{n+1}+sin(t_n)'); % adding the title to the plot

xlabel('n'), ylabel('y_n') % sdding the x and y axis labels

n = [0:9, 9800:9999]'; % n vectors

tn = t(n+1)'; % tn from first 10 and last 200

fid = fopen('tn_table.doc','w'); % opening the file to write table

fprintf(fid,'n\t\t tn\n'); % printing the title of the table in the doc

fprintf('n\t\t tn\n'); % printing the title of the table in the doc

for i = 1: length(n) % loop to print the table details

fprintf(fid,'%d\t\t %0.7f\n',n(i),tn(i)); % printing the data to file

fprintf('%d\t\t %0.7f\n',n(i),tn(i)); % printing the data to command window

end % end of loop

Screen Print of the code

2 3 4 5 6 7 8 clc; clear; % clearing the command window and workspace t = zeros(1,10000); % initilizing the t vector with all zeros t(1) = 3; % t_0 value t(2) 1; % t_1 value for n = 1:1000-2 % loop to calculate first 10000 terms t(n+2) = t(n+1) + sin(t(n)); % calculating 10000 terms of the sequence end plot(t, 'ro'); % plotting the t values as red circles title('t_{n+2} t_{n+1}+sin(t_n)'); % adding the title to the plot <label('n'), ylabel('y_n') % sdding the x and y axis labels n = [0:9, 9800: 9999]'; % n vectors tn = t(n+1)'; % tn from first 10 and last 200 fopen('tn_table.doc', 'W'); % opening the file to write table fprintf(fid, 'n\t\t tn\n'); % printing the title of the table in the doc fprintf('n\t\t tn\n'); % printing the title of the table in the doc for i = 1: length(n) % loop to print the table details fprintf(fid, '%d\t\t %0.7f\n',n(i), tn(i)); % printing the data to file fprintf("%d\t\t %0.7f\n',n(i), tn(i)); % printing the data to command window end % end of loop 1 10 11 12 13 14 15 16 17 18 19 20 fid =

Screen Print of the outputs

COMMAND WINDOW tn 0 1 2 3 4 5 6 7 8 9 9800 9801 9802 9803 9804 9805 9806 9807 9808 9809 9810 9811 9812 9813 9814 9815 9816 9817 9818 9819 9820 9821 9822 9823 9824 9825 9826 3.0000000 1.0000000 1.1411200 1.9825910 2.8916916 3.8080956 4.0554037 3.4371625 2.6453255 2.3540405 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000

Figure 1 x + tn+2 = (n+1+sin(tn) 4.5 4 POVE 3.5 3 2.5 Yn 25 1.5 18 0.5 0 0 2000 4000 6000 8000 10000 n

tn_table.docx + 1 n tn 2 0 3.0000000 3 1 1.0000000 4 2 1.1411200 5 3 1.9825910 64 2.8916916 7 5 3.8080956 8 6 4.0554037 9 7 3.4371625 10 8 2.6453255 11 9 2.3540405 12 9800 0.0000000 13 9801 0.0000000 14 9802 0.0000000 15 9803 0.0000000 16 9804 0.0000000 17 9805 0.0000000 18 9806 0.0000000 19 9807 0.0000000 20 9808 0.0000000 21 9809 0.0000000 22 9810 0.0000000 23 9811 0.0000000 24 9812 0.0000000 25 9813 0.0000000 26 9814 0.0000000 27 9815 0.0000000 28 9816 0.0000000 29 9817 0.0000000 30 9818 0.0000000 31 9819 0.0000000 32 9820 0.0000000 33 9821 0.0000000 34 9822 0.0000000 35 9823 0.0000000 36 9824 0.0000000 37 9825 0.0000000 38 9826 0.0000000 39 9827 0.0000000 40 9828 0.0000000 41 9829 0.0000000 42 9830 0.0000000 43 9831 0.0000000 44 9832 0.0000000 45 9833 0.0000000 AG 0924 AAAAAAAA