This program is using octave software. Matlab code will work

The Fibonacci sequence is given by a recursive equation Fk+1 = Fk + FR-1 with Fo = 0 and F1 = 1 i.e., the next value is the sum of previous two values i.e. {0, 1, 1, 2, 3, 5, 8, 13.....). As k gets larger, the ratio of adjacent values approaches the golden ratio given by FK lim = 1+v5 ~ 1.618033988749895... 2 k+ Fk-1 Write a for-loop (start=1, step=1, and finish=20) program of the Fibonacci sequence. Within the for-loop block, use if-command to print the following (ONLY) Golden Ratio from Fibonacci Sequence Terms added: 15 Golden Ratio Approx: 1.61803 Approximation error: 0.002% True error: 0.001% >> | Command Window Documentation Variable Editor Compute approximate answer of sin(1/3). Within the for-loop, add a command to display SN, true value of sin(tt/3), and true error result for each iteration. | A geometric series is given by N Sy = Dark = a + ar+ ar2 + ar3 +.... tarN k=0 A series is called divergent if lim Sn = cootherwise it is called convergent. a. Write a program to show that series with a=1 and r=2 is divergent. (Hint: Make N very large e.g., 500] b. Write a program to show that series with a=l and r=0.5 converges. The Fibonacci sequence is given by a recursive equation Fk+1 = Fk + FR-1 with Fo = 0 and F1 = 1 i.e., the next value is the sum of previous two values i.e. {0, 1, 1, 2, 3, 5, 8, 13.....). As k gets larger, the ratio of adjacent values approaches the golden ratio given by FK lim = 1+v5 ~ 1.618033988749895... 2 k+ Fk-1 Write a for-loop (start=1, step=1, and finish=20) program of the Fibonacci sequence. Within the for-loop block, use if-command to print the following (ONLY) Golden Ratio from Fibonacci Sequence Terms added: 15 Golden Ratio Approx: 1.61803 Approximation error: 0.002% True error: 0.001% >> | Command Window Documentation Variable Editor Compute approximate answer of sin(1/3). Within the for-loop, add a command to display SN, true value of sin(tt/3), and true error result for each iteration. | A geometric series is given by N Sy = Dark = a + ar+ ar2 + ar3 +.... tarN k=0 A series is called divergent if lim Sn = cootherwise it is called convergent. a. Write a program to show that series with a=1 and r=2 is divergent. (Hint: Make N very large e.g., 500] b. Write a program to show that series with a=l and r=0.5 converges