Use the sequence {−1,171,875;−234,375;−46,875;−9375,…} to answer the question.


What is the explicit rule that describes the sequence?


an=−1,171,875(125)n−1

an=1,171,875(−15)n−1

an=−1,171,875(15)n−1

an=1,171,875(−115)n−1

Answer:

an = −1,171,875(1/5)^n-1

Step-by-step explanation:

The given sequence is geometric sequence since they have the same common ratio r. The nth term of a geometric sequence is expressed as;

an = ar^n-1

n is the number of terms

r is the common ratio

a is the first term

From the sequence;

a = −1,171,875

r = −234,375 /−1,171,875 = -46,875/−234,375 = 0.2

r = 1/5

Substitute the values in the formula;

an = −1,171,875(1/5)^n-1

Hence the required explicit formula is an = −1,171,875(1/5)^n-1

The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The sequence is {−1,171,875;−234,375;−46,875;−9375,…}

The given sequence is the geometric sequence since they have the same common ratio r. Then the nth term of the geometric sequence will be

[tex]\rm a_n = a\ r^{n-1}[/tex]

Where

Number of terms (n)

First-term (a) = -1,171,875

Common ratio (r) = 1/5

Then nth term will be

[tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]

The explicit rule that describes the sequence is [tex]\rm a_n = -1,171,875 (\dfrac{1}{5})^{n - 1 }[/tex]. Then the correct option is C.

More about the sequence link is given below.

https://brainly.com/question/21961097

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