Sequences and Systems

Sequences

100

Write the equation:

6, 2, -2, -6, -10 

t(n) = -4n + 10

200

Write the equation

19,  22.8,  27.36,  32.832

t(n) = 15.83(1.2)ⁿ

300

Write the first 4 terms of the sequence

t(n) = 2 (3)ⁿ

0.66, 2, 6, 18

400

What is the 235th term in the sequence

t(n) = -19 + 3n

686

500

Given t(n) = 10n - 7

Is 89 a term in the sequence? Yes or No and EXPLAIN

No, because n can not be a decimal

Solving for a Variable

100

solve for y

4x + y = 13

y = -4x + 13

200

solve for y 

3x + 2y = 8

y = -3/2x + 4

300

Solve for y

-6x - y = -12

y = -6x + 12

400

Solve for x

xy + c = a

x = (a - c)/y

500

Solve for x

2(x + y) = b

x = b/2 -y

Graphing

100

Graph to find the solution

y = 1/2x + 2

y = 2x - 4 

(4,4)

200

Graph to find the solution

y = 2x + 1

y = -1x + 4

(1,3)

300

Graph to find the solution

y = 3x 

y = -x - 8

(-2,-6)

400

Graph to find the solution

2x + 3y = 12

y = x - 1

(3,2)

500

Graph to find the solution

y = 3x + 5

y - 3x = -2

no solution

Equal Values

100

y = 2x + 5

y = 4x - 1

(3,11)

200

y = -3x + 10

y = 2x - 5 

(3,1)

300

y = 1/2x + 6

y = x + 2

(8,10)

400

x = 3y - 7

x = -y + 9

(5,4)

500

y = 2x + 4

y = 2(x+2) 

infinite solutions

Substitution

100

y = 3x

2x + y = 10

(2,6)

200

5x + 3y = -1

y = -2x + 1

(4,-7)

300

x = 2y + 1

3x + 4y = 23

(5,2)

400

3x - 2y = 8

y = x - 3

(2,-1)

500

6x - 2y = 12

y = 3x + 5

no solution