Find an example of an arithmetic sequence that has an explicit pattern. Then determine the formula for that sequence and use it to define the given term.

11)

5, -5, -15, -25,  ...

-5-5 = -10;   -15-(-5) = -10;   -25-(-15) = -10   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 10 less than previous one)

difference:  d = -10

first term:  a = 5

so the formula:

and:

12)

19, 26, 33, 40,  ...

26-19 = 7;   33-26 = 7;   40-33 = 7   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 7 more than previous one)

difference:  d = 7

first term:  a = 19

so the formula:

and:

13)

-20, -29, -38, -47,  ...

-29-(-20) = -9;   -38-(-28) = -9;   -47-(-38) = -9   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 9 less than previous one)

difference:  d = -9

first term:  a = -20

so the formula:

and:

11)

1, -2, 3, -4,  ...

-5-1 = -3;   3-(-2) = 5 ≠ -3   ⇒  this is NOT an example of arithmetic sequence

however it has explicit patern:

so:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".