Question

help me pls
write an explicit formula for the sequence determined by the recursion formula
t1= -2; tn= t^(n-1) -3

Answer 1

Do you mean
\[\begin{cases}t_1=-2\\t_n=t_{n-1}-3\end{cases}\]

Answer 2

That's almost certainly a correct interpretation. Let's work out the first few values.
First, let's find \(t_1\):
\[t_1 = -2\]by definition, doesn't get much easier than that!

Next we'll find \(t_2\):
\[t_2 = t_n,\ n = 2\]but \[t_n = t_{n-1} -3\]so \[t_2 = t_{2-1} -3 = t_1 -3 = -2-3 = -5\]
Now let's find \(t_3\):
\[t_3 = t_{3-1}-3 = t_2 - 3 = -5 -3 = -8\]And \(t_4\):
\[t_4 = t_{4-1}-3 = t_3-3 = -8 -3 = -11\]I hope you see the pattern by now!

Is that an arithmetic or geometric sequence? Do you know how to write a non-recursive definition for it?