Please evaluate this question. 10 points!!
2 answers:
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Answer:
The required recursive formula is:
Step-by-step explanation:
We are given a geometric sequence as:
6,-18,54,-162,.....
Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.
Let represents the nth term of the sequence.
This means that:
As the common ratio is -3.
so,
Hence, the required recursive formula for the geometric sequence is:
Let as described in the problem statement. Plugging in
and
gives us the equations
and
Since
are nonzero, we divide the second equation by the first to get
which means that
after taking the cube root. Plugging this value for
into the first equation, we now have
Solving gives
and our desired exponential equation is