Could you plz help me with this question?

(a) t_n = 3n - 9

(b) t_16 = 39

Step-by-step explanation:

(a)

-3 - (-6) = -3 + 6 = 3

The common difference is 3.

t_1 = -6

t_2 = -6 + 3

t_3 = -6 + 3 + 3

t_4 = -6 + 3 + 3 + 3

t_n = -6 + 3(n - 1)

t_n = -6 + 3n - 3

t_n = -9 + 3n

t_n = 3n - 9

The formula is: t_n = 3n - 9

(b) t_16 = 3(16) - 9 = 48 - 9 = 39

an = -6 + 3(n - 1)

a(16) = 39

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Our d (common difference) is +3

Our a1 (First term) is -6

To find a(16) (the 16th term), plug in 16 for n.

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9