9514 1404 393
Answer:
-108
Step-by-step explanation:
About the easiest way to do this for small values of n is to compute each of the terms using the given recurrence relation.
[tex]a_1=4\\\\a_2=-3a_1=-3(4)=-12\\\\a_3=-3a_2=-3(-12)=36\\\\a_4=-3a_3=-3(36)=-108\\\\\boxed{a_4=-108}[/tex]
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Alternate solution
You recognize that the recurrence relation describes a geometric sequence with a first term of 4 and a common ratio of -3. The n-th term of a geometric sequence is ...
[tex]a_n=a_1\cdot r^{n-1} \qquad\text{for first term $a_1$ and common ratio $r$}[/tex]
Then the 4th term will be ...
[tex]a_4=4\cdot(-3)^{4-1}=4\cdot(-27)=-108[/tex]
