Respuesta :

Answer:

[tex]a_n=19+(n-1)(-5)[/tex]

Step-by-step explanation:

The explicit formula for an arithmetic sequence is [tex]a_n=a_1+(n-1)d[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term and [tex]d[/tex] is the common difference.

In this problem, we can see that the first term of the sequence is [tex]a_1=19[/tex] and the common difference is [tex]d=-5[/tex] since 5 is being subtracted each consecutive term.

Therefore, the explicit formula that describes the given arithmetic sequence is [tex]a_n=19+(n-1)(-5)[/tex]

RedGeek2531

Answer:

option 2

Step-by-step explanation:

Let { a1, a2, a3, a4, ... } be the sequence.

now the 1st term (a1) will have a value when n = 1.

similarly, all the other terms will have the values given when we substitute their respective n values into the explicit formula or fibonacci sequence.

thus, check if the 1st term is 19 by using option 2

an = 19 + (n-1)(-5)

an = 19 + (n-1)(-5) ....n = 1

an = 19 + (n-1)(-5) ....n = 1 a1 = 19 + (1-1)(-5) = 19 + 0 = 19. so it's accurate so far.

next, check a2 where n = 2.

a2 = 19 + (2-1)(-5) = 19 - 5 = 14. ....

n = 3

a3 = 19 + (3-1)(-5) = 19 - 10 = 9.

hence the conclusion from this pattern.

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