Answer:
[tex]\text{Recursive rule: }a_n=\dfrac{1}{4}a_{n-1};\ a_1=12\\\\\text{Explicit rule: }a_n=12\left(\dfrac{1}{4}\right)^{n-1}[/tex]
Step-by-step explanation:
Recursive Rule
For a geometric sequence with first term a1 and common ratio r, the recursive rule is always ...
a[n] = r×a[n-1], a[1] = a1
For your first term a1 = 12 and common ratio r = 1/4, the recursive rule is ...
a[n] = (1/4)×a[n-1], a[1] = 12
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Explicit Rule
For the same geometric sequence, the explicit rule is ...
a[n] = a1×r^(n-1)
For your sequence, the explicit rule is ...
a[n] = 12×(1/4)^(n-1)
