Respuesta :
Answer:
60(1/5)^(n-1).
Step-by-step explanation:
The common ratio r is 12/60 = 12/5 / 12 = 12/25 / 12/5 = 1/5.
The first term a1 = 60 so the explicit rule is
a1 * r^(n-1)
= 60(1/5)^(n-1).
aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .This can be obtained by using the formula of geometric sequence.
What is a geometric sequence?
Sequence is s collection of objects in a particular order and repetitions are allowed.
Geometric Sequence:
- a, ar, ar¹, ..., arⁿ⁻¹ is a geometric sequence, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.
- Common ratio, r = aₙ/aₙ₋₁
In the given question, first term a=60
Common ratio r = a₂/a₁ = 12/60 = 1/5 ⇒ r = 1/5
By definition, arⁿ⁻¹ = (60)(1/5)ⁿ⁻¹ is the required explicit rule for the geometric sequence.
Hence aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .
Learn more about geometric sequence here:
brainly.com/question/2959141
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