ARITHMETIC SEQUENCES

Common Difference

100

2, 4, 6, 8, ...

d = 2

200

7, 12, 17, 22, 27, ...

d = 5

300

35, 32, 29, 26, ... 

d = -3

400

-3, -23, -43, -63, ... 

d= -20 

500

12, -1, -14, -27, ... 

d= -13 

Next Three Terms

100

2, 4, 6, 8,...

10, 12, 14

200

7, 12, 17, 22, 27, ...

32, 37, 42

300

35, 32, 29, 26, ... 

23, 20, 17

400

-3, -23, -43, -63, ... 

-83, -103, -123

500

12, -1, -14, -27, ... 

-40, -53, -66

Recursive Form

100

37, 39, 41, 43, 45, ... 

a_n = a_n-1 + 2 

200

17, 40, 63, 86, 109, ...

a_n = a_n-1 + 23

300

102, 87, 72, 57, ... 

a_n = a_n-1 + -15

400

-8, -14, -20, -26, ... 

a_n = a_n-1 + -6

500

-17, -11, -5, 1, ... 

a_n = a_n-1 + 6

Explicit Form

100

9, 14, 19, 24, ... 

a_n = 9 + 5(n-1) 

200

13, 11, 9, 7, ... 

a_n = 13 + -2(n-1)

300

-30, -40, -50, -60, ...

a_n = -30 + -10(n-1)

400

-34, -64, -94, -124, ... 

a_n = -34 + -30(n-1)

500

-7, 2, 11, 20, ... 

a_n = -7 + 9(n-1)