#include<iostream>
#include<vector>
#include<cassert>
using namespace std;
// Returns a vector of Fibonacci numbers from start to max.
// Sequence A000045 in OEIS if start is 0.
vector<unsigned> fibonacci (const unsigned start, const unsigned max)
{
// Invariants:
if (1<start)
throw std::range_error
("vector<unsigned> fibonacci (const unsigned start, const unsigned max): start < 1");
if (max<start)
throw std::range_error
("vector<unsigned> fibonacci (const unsigned start, const unsigned max): max < start");
// Empty set...
vector<unsigned> fib {};
if (max)
{
// First term...
fib.push_back (start);
if (1<max)
{
// Second term...
fib.push_back (1);
// All remaining terms...
unsigned next = 0;
while ((next = fib.back()+fib[fib.size()-2]) <= max)
fib.push_back (next);
}
}
return fib;
};
// Return true if the given number is prime.
bool is_prime (const unsigned num)
{
if (num<2) return false;
if (!(num%2)) return num==2;
for (unsigned div=3; div<=sqrt(num); div+=2)
if (!(num%div)) return false;
return true;
}
// Displays all prime Fibonacci numbers in range [1:10,000].
int main()
{
const unsigned max=10000;
vector<unsigned> f = fibonacci (1, max);
cout << "Prime Fibonacci numbers in range [1:" << max << "]\n";
for (auto n : f)
if (is_prime (n))
cout << n << ", ";
cout << "\b\b " << endl; // backspace and overwrite trailing comma
}
#include<iostream>
#include<vector>
#include<cassert>
using namespace std;
// Returns a vector of Fibonacci numbers from 0 to the nth term.
// Sequence A000045 in OEIS.
vector<unsigned> fibonacci (const unsigned terms)
{
// Empty set...
vector<unsigned> fib {};
if (terms)
{
// First term...
fib.push_back (0);
if (1<terms)
{
// Second term...
fib.push_back (1);
// All remaining terms (2 to n-1).
for (unsigned term=2; term<terms; ++term)
fib.push_back (fib[term-2]+fib[term-1]);
}
}
return fib;
};
// Displays Fibonacci sequence to 10 terms followed by the 20th term.
int main()
{
const unsigned max=20;
vector<unsigned> f = fibonacci (max);
assert (f.size()==max);
cout << "Fibonacci Sequence\n10 terms: ";
for (unsigned n=0; n<10; ++n)
cout << f[n] << ", ";
cout << "\b\b "; // backspace and overwrite trailing comma
cout << "\n20th term: " << f[max-1] << std::endl;
}
You can use a loop statement to input the numbers. Here is a code snippet:
int i, arr[10];
cout<<"Enter the 10 numbers: ";
for( i=0; i<10; i++)
cin>>arr[i];//Inserting the elements in the array
In a Fibonacci sequence, sum of two successive terms gives the third term.... here is the Fibonacci sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144........ General formula to generate a Fibonacci sequence is """Fn= Fn-1 + Fn-2""" To check whether a number is Fibonacci or not follow the following steps: 1) Get the number as input from user. 2) Fix the first two numbers of sequence as 0 and 1. 3) put a sentinel loop with upper limit being the input number. 4)in the body of loop generate the next number in sequence in each iteration and continue swapping the values as follows: a=0 b=1 next=a+b while (next< input) a=b b=next next=a+b wend 5) lastly when program exits the loop compare the last number of sequence with the input number if they are equal then number is Fibonacci otherwise not. otherwise the last term of sequence will be less than the input number.
It is a term for sequences in which a finite number of terms are defined explicitly and then all subsequent terms are defined by the preceding terms. The best known example is probably the Fibonacci sequence in which the first two terms are defined explicitly and after that the definition is recursive: x1 = 1 x2 = 1 xn = xn-1 + xn-2 for n = 3, 4, ...
#include<stdlib.h> #include<conio.h> #include<stdio.h> void main (void) { clrscr(); int i; int a[10]; a[0]=0; a[1]=1; printf("First 10 Fibonacci numbers are :\n"); printf("%d\n%d\n",a[0],a[1]); for(i=2;i<10;i++) { a[i]=a[i-1]+a[i-2]; printf("%d\n",a[i]); } getch(); }
void main() { int n,old=0,curr=1,new=0; clrscr(); printf("enter the total number of terms up to which you want to print the Fibonacci series"); scanf("%d",&n); printf("%d",old); printf("\n%d",curr); for(i=1;i<=n;i++) { new=old+curr; old=curr; curr=new; printf("\n%d",new); } getch(); }
#include<stdio.h> #include<conio.h> int fib(int a); main() { int a; clrscr(); scanf("%d",&a); for(int i=0;i<a;i++) printf("%d\n",fib(i)); } int fib(int a) { if(a==0) return 0; if(a==1) return 1; else return (fib(a-1)+fib(a-2)); }
No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant
0,1,1,2,3,5,8,13
If the Fibonacci sequence is denoted by F(n), where n is the first term in the sequence then the following equation obtains for n = 0.
Fibonacci sequence
No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.
Fibonacci sequence
They are: 10 and 16
34-55-89 are.
NO, its not a Fibonacci Sequence, but it is very close. The Fibonacci Sequence is a series of numbers in which one term is the sum of the previous two terms. The Fibonacci Sequence would go as follows: 0,1,1,2,3,5,8,13,21,..... So 0+1=1, 1+1=2, 1+2=3, 2+3=5, ans so on.
The answer depends on the sequence. The ratio of terms in the Fibonacci sequence, for example, tends to 0.5*(1+sqrt(5)), which is phi, the Golden ratio.
The Fibonacci sequence starts with 1 and 1. However any sequence in which the first two terms are given and the rest are defined recursively as t(n) = t(n-2) + t(n-1), with n = 3, 4, ... is also known as a Fibonacci sequence. Note the "the" and "a" preceding Fibonacci sequence.