Send help please, i struggled with these kinds of questions minutes ago!

  5 +4(n -1)

Step-by-step explanation:

The wording "the same number of sticks is added each time" tells you this is an arithmetic sequence. To find the rule, you need to know ...

The form of the rule for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . . . a1 = first term; d = common difference

For a1 = 5 and d = 4, your rule for the n-th pattern is ...

  sticks in n-th pattern = 5 +4(n -1)

This can be simplified to 1 +4n.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is