recently, I have been learning, arthimitic progression and series and also geometric progression and series. When searching the internet for extra study material I came across a formula for changing difference: nth term: [itex] a + (n - 1)d + ½(n - 1)(n - 2)c [/itex]. I would really like to know how this formula was derived cant find the proof on the internet, just the formula. I have even tried myself have no luck. I can see the first part [itex] a+(n-1)d [/itex] as AP but after that a bit of confusion I have a felling it has to do with a quadratic only because, the example the formula has been applied to is a quadratic sequence. I did read on purple maths, that to understand the real method on solving a quadratic sequence, you have to understand calculus to a certain extent, unfortunally I have only just started reading calculus so I lack allot of knowledge in that specific area, which makes me think the formula was derived from a calculus equation; correct or not ? I would really appreciate any insight into this formula, for example shown how it was derived, what the formula is called and if there is any text or web sites that I can be pointed to understand this more. Thanks in advanced for any input; much appreciated.