Question

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

Answer 1

Answer:

$f_n=7+\left(-2\right)\left(n-1\right)$

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  

$f_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$5-7=-2,\:\quad \:3-5=-2,\:\quad \:1-3=-2$

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

$d=-2$

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

$f_n=a_1+\left(n-1\right)d$

$f_n=7+\left(-2\right)\left(n-1\right)$

Therefore, option C is true.