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.
PLEASE PLEASE REPLY BY THURSDAY
THANKS SO MUCH
p.s dont worri about the underlines. i onli did it to aline the numbers
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.
PLEASE PLEASE REPLY BY THURSDAY
THANKS SO MUCH
p.s dont worri about the underlines. i onli did it to aline the numbers
Hello,
1. you easily can detect that
This is called a recursive definition of the serie s.Code:s_(n+1) = s_n + n
To calculate with this equation isn't very useful.
2. I'll arange the numbers of the serie and calculate the differences:
You see that the serie is an arithmetic serie of order 2. Therefore the general equation is:Code:1 3 6 10 15 21 28 36 ... 2 3 4 5 6 7 8 1 1 1 1 1 1
s_n = a*nē + b*n + c
Now plug in the values of s_1, s_2 and s_3:
Solve this system of simultaneous equations. I've got: a = 1/2, b = 1/2, c = 0Code:1 = a + b +c 3 = 4a + 2b + c 6 = 9a + 3b + c
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
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.
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
also fibbonaci this wikipedia page seems like a good page for you to formulate your answer from
Triangular number - Wikipedia, the free encyclopedia