Problem:
Find the formula for $n^{th}$ term of the sequence $-1, 0, 2, 6, 14, 30 \ldots$
I identified that the difference is the double of the previous
i.e 1, 2, 4, 8, 16
How would I use this to find the formula if I was to asked to find the $50^{th}$ or even the $100^{th}$ term?
Any help would be appreciated.
Best Answer
As stated in the comments the $n$th term is $$a_n=2^n-2=2(2^{n-1}-1)$$
Edit: one can also conclude that the sequence follows any pattern the user desires with adequate reasoning, so this question therefore cannot have a 'correct' answer without being supplied with infinite terms of the series.