What is the explicit rule for the arithmetic sequence shown in the graph?

Step-by-step explanation:

Looking at the given graph, the slope of the line is expressed as

Slope = (y2 - y1)/(x2 - x1)

y2 = 19.5

y1 = 9.5

x2 = 6

x1 = 1

Slope = (19.5 - 9.5)/(6-1)

Slope = 10/5 = 2

The successive terms is increasing by 2

The formula for the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a is the first term of the sequence

n is the number of terms in the sequence.

d is the common difference.

From the information given,

a = 9.5

Tn = an

d = 2

The explicit rule for the arithmetic sequence will be

an = 9.5 + 2(n-1)

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2