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|dw:1443915861353:dw|

the jump from 1 to 3 is +2
|dw:1443915905024:dw|

the jump from 3 to 6 is +3
|dw:1443915932403:dw|

the jump from 6 to 10 is +4
|dw:1443915954079:dw|

the jump from 10 to 15 is +5
|dw:1443915976631:dw|

I want an explicit formula

|dw:1443916308731:dw|

the general quadratic is ax^2 + bx + c

we now have this system of equations
a+b+c = 1
4a+2b+c = 3
9a+3b+c = 6

I am still here

do you know how to solve for a,b,c?

you have a number of options
1) elimination
2) substitution
3) matrices

Dude. Like, That is totally different from what I am taught by the book

i contend that it can be any value we want it to be if there are no other conditions for the sequence.

@Karon86 how does the book show you? what method do they use?

A3: 1+2+3 = 6
A4: 1+2+3+4=10

A5:1+2+3+4+5=15
An: 1+2+...+n

Are you still here

I see, let me think

can you find an explicit formula for An: 1+2+...+n

Why is it that way?

I am confused with what comes after therefore

notice how the n pairs with 1, n-1 pairs with 2, n-3 with 3, etc etc

I don't understand

do you have access to a laptop or desktop computer?

No sir but if I can acces it on my phone. God I wish I had a laptop of desktop