Given that the first term is LaTeX: t_1=2t 1 = 2, and the recursive definition is LaTeX: t_{n+1}=3^{\left(t_n\right)}t n + 1 = 3
( t n ), what would be the 2nd term (LaTeX: t_2t 2).
2 answers:
You might be interested in
1. Perhaps the simplest rule is one that makes this the start of an arithmetic sequence:
Then the sequence will continue ...
... 3, 5, 7, 9, 11, 13, 15, ...
2. We can multiply the two terms by some values, add the results, then add some constant. There are an infinite number of ways to choose such values. Here's one set of numbers that give the third term from the first two:
Then the sequence will continue ...
... 3, 5, 7, 13, 15, 37, 23, ...
3. We can multiply adjacent values and add a constant.
Then the sequence will continue ...
... 3, 5, 7, 28, 188, 5256, 988120, ...