Originally Posted by

**Fibonacci** x: 1__2__3__4__5__6__7

y: 1__3__6__10_15_21_28

can anyway find the rule of this table?? please also explain if possible.

...

Hello,

1. you easily can detect that

This is called a recursive definition of the serie s.

To calculate with this equation isn't very useful.

2. I'll arange the numbers of the serie and calculate the differences:

Code:

1 3 6 10 15 21 28 36 ...
2 3 4 5 6 7 8
1 1 1 1 1 1

You see that the serie is an arithmetic serie of order 2. Therefore the general equation is:

s_n = a*nē + b*n + c

Now plug in the values of s_1, s_2 and s_3:

Code:

1 = a + b +c
3 = 4a + 2b + c
6 = 9a + 3b + c

Solve this system of simultaneous equations. I've got: a = 1/2, b = 1/2, c = 0

Therefore your serie has the equation:

s_n = 1/2*nē + 1/2*n

To check, calculate s_7 = 1/2*49 + 1/2*7 = 56/2 = 28

EB