Fibonacci sequnce has this pattern:
1,1,2,3,5,8,13,21,34,55,......
each number is achieved by adding the previous number to the current number (1+1=2, 2+1=3, 3+2=5,....)
List the first eight terms of the sequence formed by finding the differences of successive terms.
1-1 = 0
2-1 = 1
3-2 = 1
5-3 = 2
8-5 = 3
13-8= 5
21-13=8
34-21=13 looks like it is going to do the Fibonacci sequence again
To find the differences of successive terms in the Fibonacci sequence, you can subtract each number from its preceding number. Here are the first eight terms of the sequence formed by finding the differences:
1 - 1 = 0
2 - 1 = 1
3 - 2 = 1
5 - 3 = 2
8 - 5 = 3
13 - 8 = 5
21 - 13 = 8
34 - 21 = 13
So, the first eight terms of the sequence formed by finding the differences of successive terms are:
0, 1, 1, 2, 3, 5, 8, 13
To find the differences of successive terms in the Fibonacci sequence, you need to subtract each term from the next term. Here's how to do it:
1. Take the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
2. Start with the first term, which is 1.
3. Subtract the first term from the second term:
1 - 1 = 0
4. The result, 0, is the first term in the sequence formed by finding the differences of successive terms.
5. Repeat the process for the subsequent terms:
Second term - Third term:
1 - 2 = -1
Third term - Fourth term:
2 - 3 = -1
Fourth term - Fifth term:
3 - 5 = -2
Fifth term - Sixth term:
5 - 8 = -3
Sixth term - Seventh term:
8 - 13 = -5
Seventh term - Eighth term:
13 - 21 = -8
Eighth term - Ninth term:
21 - 34 = -13
6. The resulting sequence formed by finding the differences of successive terms is: 0, -1, -1, -2, -3, -5, -8, -13.
Therefore, the first eight terms of this sequence are 0, -1, -1, -2, -3, -5, -8, -13.