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.

THANKS SO MUCH
p.s dont worri about the underlines. i onli did it to aline the numbers

2. 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
Code:
 s_(n+1) = s_n + n
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*n² + 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*n² + 1/2*n

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

EB

3. if you have the two sequences

1 2 3 4 5 6 7 ---- x
1 3 6 10 15 21 28 ---- y

the value of y is the sum of all the x values until that point

1,2,3,4,5,6,7 ----x
1,(2+1),(3+2+1),(4+3+2+1),(5+4+3+2+1),(6+5+3+3+2+1 ) (7+6+5+4+3+2+1) ----y

so at any index of x the corresponding value of y will be the sum of all the values of x upto and including that index.

so if we want to know the value of y when x = 8. the value is (8+7+6+5+4+3+2+1) = 36

I hope that makes sense.

4. sorry eb did not mean to double post but i guess we were posting at the same time. i much prefer your explanation

5. Originally Posted by chogo
sorry eb did not mean to double post but i guess we were posting at the same time. i much prefer your explanation
Hello, Chogo,

you are welcome!

I think the more different solutions a poster get the better he can understand to solve his problem.

And as you certainly have noticed it is common use at this forum that everybody publishes his version of a solution.

EB

6. This is called the triangle sequence.

The equation is,
a_n=(n)(n-1)/2

(Did you know that every positive integer is the sum of at most three triangular numbers! -Fermat).

7. thats great PH did not know that. I just read these numbers can be found in the diagonal starting at row 3 on pascals triangle