To explain my question, here is an example.
Below is an AP:
2, 6, 10, 14....n
Calculating the nth term in this sequence is easy because we have a formula. The common difference (d = 4) in AP is constant and that's why the formula is applicable, I think.
But what about this sequence:
5, 12, 21, 32....n
Here, the difference between two consecutive elements is not constant, but it too has a pattern which all of you may have guessed. Taking the differences between its consecutive elements and formimg a sequence results in an AP. For the above example, the AP looks like this:
5, 7, 9, 11.....n
So given a sequence with "uniformly varying common difference" , is there any formula to calculate the nth term of this sequence?