nth term is n^3-3
Can anyone give me a formula for the series: -2, 5, 24, 61, 122 ....
This is more of an association problem which shows my brains are fried. I'm a "has been" in the field and this posting is a total failure of my part. It is a pre Calculus 11th (junior level) grade. Got it Npower 3 -3
For those of us who aren't as sharp as biffboy, here is an "algorithmic" approach- write these as , , , , , the "first differences" are , , , and ; the "second differences" are , , and ; the "third differences" are , , and . Since the third differences are all the same, all succeeding differences are 0 and we can write this as a cubic equation.
"Newton's divided difference formula" is similar to the Taylor's series but with finite differences rather than derivatives: .
Here, that gives
There I started the indexing with n=0. Had I, instead, started with m= 1, so that n+1= m, that would be .