# Thread: What would be the equation(s) for this?

1. ## What would be the equation(s) for this?

This is really hard for me to explain.

Say I have 2 numbers, 20 and 800
20 will decreased by a constant and added to itself
(Say the constant is .2, it will be 20 + 19.8, + 19.6 etc...)
Now, How do I find the constant so that with all the numbers added will make 800?

( $x_1 + x_2 + x_3..... = 800$)

And how would I write the equation to go with that that's not as long as the one stated above this text.

If I'm not so clear on the question, I'll try to describe it better.

(Also, A quick method on adding consecutive reals together would be nice)

2. Well there are two formulas you can use for a sequence like that:

The nth term in an arithmetic progression: $x_n=a(n-1)d$
where a is the original value of the progression (20 in that case) and d is the constant (or difference) between each progression, which is a negative value in that example.

To find the sum of n terms you can use: $s_n=\frac{n}{2}(2a+(n-1)d)$

But in your case you already have the sum so you could plug 800 in and solve for n?

Been doing sequences allllll morning.