2007-04-26 22:27:35 · 20 answers · asked by paul 1 in Science & Mathematics ➔ Mathematics
3+2N+N!
The last term is "factorial", and not just punctuation.
This simple formula will give you the value of the Nth term (any term you want to choose).
You should be able to use a calculator to evaluate this expression for any Nth term you wish.
2007-04-26 22:54:24 · answer #1 · answered by Happy Helper 2 · 0⤊ 0⤋
These numbers are from the standard triangle number sequence.
The basic one is 1, 3, 6, 10, 15, 21... which has a formula for the nth term of n(n + 1)/2.
Your sequence starts two further up so the formula is (n + 2)(n+ 2 + 1)/2, that is (n+2)(n+3)/2
2007-04-28 15:27:23 · answer #2 · answered by fred 5 · 0⤊ 0⤋
Well the question was, what is the nth term, not the next one.
When you look at the terms, you see that the first one is the sum of the first three numbers (1,2,3). The second is the sum of the first 4 numbers etc. So we get: the nth term is the sum of the first n +2 Numbers. We can easily calculate the sum of the first n numbers (see Gauss): Sum of the first n numbers = (n)*(n+1)/2
So we get for this special sequence:
The nth term is exactly (n+2)(n+3)/2.
See: 6 = (1+2)(1+3)/2
10 =(2+2)(2+3)/2
15 = (3+2)(3+3)/2
and so on.
2007-04-27 06:00:28 · answer #3 · answered by idest23 2 · 0⤊ 0⤋
well we must first find the difference in each term
10 - 6 = 4
15 - 10 = 5
21-10 = 6
28-21 = 7
36-28 = 8
well we can see a patern right there, the second difference is 1.
and well it has been a while since I have done sequences so I don't really remember how to write out the answers but...
a formula for that sequence would be
((nx-nx-1)+1)+nx = nx+1
n1 = 6
n2 = 10
That isn't exactly proper notation, but it gets you the answer
(nx-1 is the nth term one before in the sequence and nx+1 is the next nx in the sequence)
anyways to find the next term you would gave
((36 -28)+1)+36 =
(8+1)+36
9+36 = 45
so the next term is 45
2007-04-27 05:44:08 · answer #4 · answered by l0uislegr0s 3 · 0⤊ 1⤋
the next no is 45 then 55 the sequence rises in numerical ie 6 to 10 is 4 10 to 15 is 5 and so on
2007-04-27 05:32:22 · answer #5 · answered by Anonymous · 1⤊ 1⤋
45
6 +4 10
10 + 5 15
15 + 6 21
21 + 7 28
28 + 8 36
36 + 9 45
etc
2007-04-27 06:42:50 · answer #6 · answered by Anonymous · 0⤊ 0⤋
The first difference :
4,5,6,7,8
The second difference :
1,1,1,1,1,1 ...
The nth term is a second degree function of n
T(n) = a n^2 + b n + c
since : T(1) =6
So: a+b+c =6................(1)
Since T(2) = 10
So: 4a+2b+c = 10.........(2)
Since T(3) = 15
9 a + 3b+c=15...............(3)
From (1), (2) & (3)
a= 1/2
b= 5/2
c = 3
So T(n) = 1/2( n^2 + 5n + 6) = 1/2 (n+2)(n+3)
2007-04-27 05:48:23 · answer #7 · answered by a_ebnlhaitham 6 · 1⤊ 0⤋
+4+5+6+7+8+9+10...etc
2007-04-27 05:32:23 · answer #8 · answered by Mr. Ree 5 · 0⤊ 1⤋
nth term=6+3(n-1)+[n(n-1)/2]
2007-04-27 08:49:30 · answer #9 · answered by Davy T 3 · 0⤊ 0⤋
6-10 =4
10-15=5
it keeps going up like this the anser is 45.
2007-04-27 05:44:01 · answer #10 · answered by pierce_banderiezz 2 · 0⤊ 0⤋