What is the equation to describe this pattern:?

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!

Thanks to the first answer...not really. This is called the homework help section for a reason. I have a 105 in math, equations don't normally stump me, but this one is like right in front of my nose but I can't get it! Grrr...

Answer 1

Although Wine From Your Tears is excellent and has aall the correct possible answers it is recursive and requires multiple definitions.

the following equation is non-recursive and does describe the behavior/pattern.

f(a) = a^2 +a/2
or
f(a) = (a * a)/2 + a/2
f(1) = (1 * 1)/2 + 1/2 =1/2 +1/2 = 2/2 = 1
f(2) = (2 * 2)/2 + 2/2 = 4/2 + 1 = 2 + 1 = 3
f(3) = (3 * 3)/2 + 3/2 = 9/2 +3/2 = 12/6 = 6
and so on...

How is this derived? Well that takes more time than I want to use.

Hope this helps.

Answer 2

for x =1, f(x)=1
for x >1, f(x)= x + f(x-1)

Using this definition f(2) = 2 + f(1)
f(2) = 2 + 1 = 3

and f(10) = 10 + f(9) = 10+ 45 = 55

Answer 3

I don't help kids with their homework! (That's what I always say when I don't know the answer).