For each explicitly-defined sequence below, write the first few terms. Then use the terms to write a recursive equation. a. t(n) = 2n + 5

b. t(n) = 3(1/2)^n

Step-by-step explanation:

Problem A

t(1) = 2(1) + 5

t(2) = 2*2 + 5 = 9

t(3) = 2*3 + 5 = 11

t(4) = 2*4 + 5 = 13

So this is the explicit result. Now try it recursively.

t_3 = t_2 + 2

t_3 = 9 + 2

t_3 = 11          which is just what it should do.

t_n = t_(n - 1) + 2

Problem B

t(1) = 3 * 1/2

t(1) = 3/2

t(2) = 3*(1/2)^2

t(2) = 3 * 1/4

t(2) = 3/4

t(3) = 3*(1/2)^3

t(3) = 3 * 1/8

t(3) = 3/8

t(4) = 3 (1/2)^4

t(4) = 3 (1/16)

t(4) = 3/16

So in general

t_n = t_n-1 * 1/2

For example t(5)

t_5 = t_4 * 1/2

t_5 = 3 /16 * 1/2 = 3/32

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.