# Thread: Turning a Sequence into an equation

1. ## Turning a Sequence into an equation

Hello to everyone, I am new to Math Forum and I hope I have posted this in the correct section.

I have a number that is generated every day from many constants. The only variable that affects the outcome is the number of times (N) the number has generated an outcome.

I sincerely apologise if I do not use correct notation but the equation is

Y = ( K + NA ) where K, A, D, X and C are all constants.
( DX +NDC )

I need to work out an equation that for a given number of outputs (N) I can work out the average of all the outputs.

So if I had got N=2 the equation would be:

1 * ( K + NA ) + ( K + (N-1)A ) + ( K + (N-2)A )
3 ( DX +NDC ) ( DX +(N-1)DC ) ( DX +(N-2)DC )

The last three sections should be in large brackets. I cannot work this out for 'n' number of times where I do not know what 'n' is.

I am really sorry if this is not in the right section but I have gone as far as I can with this and I am not sure if I need calculus, integration, differentiation or what so I apologise again if this is not in the correct section.

2. Originally Posted by SteveI
Hello to everyone, I am new to Math Forum and I hope I have posted this in the correct section.

I have a number that is generated every day from many constants. The only variable that affects the outcome is the number of times (N) the number has generated an outcome.

I sincerely apologise if I do not use correct notation but the equation is

Y = ( K + NA ) where K, A, D, X and C are all constants.
( DX +NDC )

I need to work out an equation that for a given number of outputs (N) I can work out the average of all the outputs.

So if I had got N=2 the equation would be:

1 * ( K + NA ) + ( K + (N-1)A ) + ( K + (N-2)A )
3 ( DX +NDC ) ( DX +(N-1)DC ) ( DX +(N-2)DC )

The last three sections should be in large brackets. I cannot work this out for 'n' number of times where I do not know what 'n' is.

I am really sorry if this is not in the right section but I have gone as far as I can with this and I am not sure if I need calculus, integration, differentiation or what so I apologise again if this is not in the correct section.
Is this the sum?
$
\dfrac{1}{M} \sum_i^M
\dfrac{( K + A(N-i)}{DX + DC(N-i)}
$

If that is the case then it can be handled piecewise.
.