Which sequence could be described by the recursive definition: LaTeX: t_{n+1}=\:-1\cdot t_n+3t n + 1 = − 1 ⋅ t n + 3
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To solve this we are going to use the formula for the nth term of a geometric sequence: 
where
is the nth term
is the first term
is the common ratio
is the place of the term in the sequence
Notice that we can infer for our problem that
and 
.
Now, to find our common ratio, we are going to use the formula
where
is the current term in the sequence
is the previous term in the sequence
for
and 
:
Since
, we can conclude that 
.
Notice that the first therm of our geometric sequence is -5, so
. Since , we can conclude that 
.
We can conclude that the values of B and C in our geometric sequence are: and .
where
Notice that we can infer for our problem that
Now, to find our common ratio, we are going to use the formula
where
for
Since
Notice that the first therm of our geometric sequence is -5, so
We can conclude that the values of B and C in our geometric sequence are: