Equation Help!?

Question

1=1
2=3
3=6
4=10
5=15
6=21
7=28
8=36
9=45
10=55
etc.

All answers are appreciated, thank you! I'm completely stumped! I need an equation with one variable to describe this pattern.

Thanks, but I get the sequence. I just need the equation. I can't get that part.

Thanks you to the second answer. It works!

Answer 1

(x^2 + x) / 2

Answer 2

Let An = the missing value
An-1 = the number in the sequence before the missing
value
n = the number of the missing term

For your situation,

A1 = 1, n=1
A2 = 3, n=2, A2-1=A1

For the general term An

An= An-1 + n

Answer 3

add 2,3,4,5,6,... to the previous
1=1
2=1+2=3
3=3+3=6
4=6+4=10
5=10+5=15
6=15+6=21
and so on

Answer 4

equation 1 3 6 10 15 21 28 36 45 55
^ ^ ^ ^ ^ ^ ^ ^ ^
diff 1 2 3 4 5 6 7 8 9 10
equat-diff ^ ^ ^ ^ ^ ^ ^ ^
1 1 1 1 1 1 1 1 1
try 0.5n^2+1
Answers 0.5n^2+1

Answer 5

These are so-called 'triangular numbers'.
1 = a single line of one dot
*
3 = a line of one dot, above a line of 2 dots
*
**
6 = a line of one dot, above a line of 2, above a line of 3
*
**
***
etc.

You see this, yes? OK, here's the next step: Put two of these triangles next to each other, but flip one upside down:

Two triangles of size 1:
* *

Two triangles of size 2:
* **
** *

Two triangles of size 3:
* ***
** **
*** *

Voila! You have rectangles of size n*(n+1)
But each rectangle consists of *two* triangles, whereas you only want one.

Hence, the formula is (n*(n+1))/2.

Hope that helps!

Answer 6

the pattern is following SEQUENCE:
A(n)=A(n-1)+n; A(1)=1 n=1,2,3,...
or A(n)=(n(n+1))/2

Answer 7

the answers are going up in number order 2,3,4,5,6,7,8,9,10,the next answer is11=66,12=78 and so

Answer 8

the answers is in two ways
[n*(n+1)]/2
or
(n^2+n)/2
both are same........bye