2006-12-15 17:04:57 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Formula to find n
2006-12-15 17:07:56 · update #1
The pattern seems to be:
a[1] = 6
a[n] = a[n - 1] + (n+2)
But that's in the form of a recursive sequence and we want a closed form.
The points (1,6), (2,10), (3, 15), and so forth don't have a linear relationship. We have to suspect it's a quadratic relationship.
Let f(x) = ax^2 + bx + c. f(1) = 6, f(2) = 10, f(3) = 15, and we can make three equations out of this.
a + b + c = 6
4a + 2b + c = 10
9a + 3b + c = 15
I won't show you the details of how the system of equations was solved, but
a = 1/2, b = 5/2, c = 3
So our function f(x) = (1/2)x^2 + (5/2)x + 3
Therefore
a[n] = (1/2)n^2 + (5/2)n + 3, which we can change to
a[n] = [n^2 + 5n + 6]/2 = [(n + 3)(n + 2)]/2
2006-12-15 17:21:52 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
The nth term in the sequence is the sum of the numbers 1 thru n+2, so the formula for the nth term in the sequence is:
(n+2)(n+3)/2
2006-12-15 21:01:02 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
S = (n+2)(n+3)/2
2006-12-15 17:10:16 · answer #3 · answered by Scythian1950 7 · 2⤊ 0⤋
I love series...
Tn = T(n-1)+(n+2)
Here is why:
Each term is the pervious term plus an increasing number, starting with 4 on the second term. So, T(n-1) is the previous term and the additive is equal to n+2.
Does that work or does it need to be independent of the previous? If so, good luck, because I don't want to think that hard.
2006-12-15 17:15:48 · answer #4 · answered by Mike J 3 · 0⤊ 4⤋
45
2006-12-15 17:06:28 · answer #5 · answered by Anonymous · 0⤊ 3⤋
It's YOUR homework isn't it?
2006-12-15 17:06:07 · answer #6 · answered by Anonymous · 0⤊ 3⤋