# How to write another expression (for n) when given a series sum?

## Homework Statement

Sorry if the question sounds a bit off, i wasnt quite sure how to word it.

My math question is: given the expression Sn=n^2 + 2n, determine an expression, in simplified form, for Sn-1 in terms of n.

## Homework Equations

NA (i dont think there are any equations for this)

## The Attempt at a Solution

First three terms are 3, 8 and 15. All of which have a different 'common ratio' when 8 is divided by 3, its 2.67 but when 15/8 its 1.875?
Which confuses me further, and as for the original question, no idea how to proceed.

Any help is much appreciated, thanks.

try substituting n-1 for in in the expression for S(n) and then simplifying the result.

Mentallic
Homework Helper
My math question is: given the expression Sn=n^2 + 2n, determine an expression, in simplified form, for Sn-1 in terms of n.

First three terms are 3, 8 and 15. All of which have a different 'common ratio' when 8 is divided by 3, its 2.67 but when 15/8 its 1.875?
Which confuses me further...

Well of course the ratios aren't the same! It's a quadratic! Not a linear equation...

Its not a case of dividing the n-1 by n as it is a ascending arithmetic method as the difference keeps increasing by 2:

1 2 3
3 8 15

8-3 = 5, 15-8 = 7, so the next difference will equal 9 then 11 and so on an so forth, so your equation is essentially using the "box" number, 1 2 3, to get the actual number in the formula

So if Sn=n^2 + 2n, Sn-1 means you have to rewrite the formula in terms of the previous number