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Use the graph to write the explicit rule of the arithmetic sequence.


A) 
ƒ(n) = 3 + 1(n – 1)

B) 
ƒ(n) = 7 + 3(n – 1)

C) 
ƒ(n) = 7 + (–2)(n – 1)

D) 
ƒ(n) = 2 + (–7)(n – 1)

Use the graph to write the explicit rule of the arithmetic sequence A ƒn 3 1n 1 B ƒn 7 3n 1 C ƒn 7 2n 1 D ƒn 2 7n 1 class=

Respuesta :

absor201

Answer:

[tex]f_n=7+\left(-2\right)\left(n-1\right)[/tex]

Therefore, option C is true.

Step-by-step explanation:

From the graph, we get the sequence

7, 5, 3, 1, ...

Here,

a₁ = 7 is the first element.

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]f_n=a_1+\left(n-1\right)d[/tex]

computing the differences of all the adjacent terms

[tex]5-7=-2,\:\quad \:3-5=-2,\:\quad \:1-3=-2[/tex]

The difference between all the adjacent terms is the same and equal to

[tex]d=-2[/tex]

substituting a₁ = 7 and d = -2 in the nth term of the sequence

[tex]f_n=a_1+\left(n-1\right)d[/tex]

[tex]f_n=7+\left(-2\right)\left(n-1\right)[/tex]

Therefore, option C is true.

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