1. Consider the Fibonacci sequence. (Fibonacci sequence starts from 1. Please in

Question

1. Consider the Fibonacci sequence. (Fibonacci sequence starts from 1. Please include both the codes and the OUTPUT)

(1). Write a ‘for’ loop to generate the Fibonacci sequence, and print out the rst ten terms;

(2). Derive a closed form for the Fibonacci sequence(You just write your nal results into word document, and no steps are needed);

(3). Create a vector bProd where each element of bProd is the product of two consecutive Fibonacci numbers;

(4). Create a vector partialSum where each element partialSum is a partial sum of the sequence of squares of Fibonacci numbers; Do you observe some-thing comparing (3) and (4)?

(5). Create a vector r where each element r is the ratio of consecutive Fi-bonacci numbers: r = [f0/f1 f1/f2 · · · fn1/fn]. What do you notice about the elements of r?

Explanation / Answer

A ‘for’ loop to generate the Fibonacci sequence, and print out the rst ten terms;-

int a=1;
int b=1;
int c;
int count=10; // To generate the Fibonacci Series upto the first ten terms
System.out.print(a+" "+b);   
  
for(int i=2;i<count;i++)
{
c = a + b;
System.out.print(" "+c);
a = b;
b = c;
}

Output:-

1 1 2 3 5 8 13 21 34 55

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.