Arithmetic and Geometric Sequences Formulas

Create the explicit formula for the sequence: 2, 8, 14, ...

• a_n=2+6n

• a_n=-6+6n

• a_n=6n-4

• a_n=4-6n

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

• a₁= 10

  a_n= a_n-1 - 5

• a₁= 10

  a_n= a_n-1 + 5

• a₁= 10

  a_n= a_n (5)

• a₁= 10

  a_n= a_n-1 (5)

• Sequence

• Recursive Formula

• Explicit Formula for an Arithmetic Sequence

• Explicit Formula for a Geometric Sequence

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11
  a₁=6

• a_n=a_n-1-4
  a₁=6

• a_n=a_n-1+9
  a₁=6

• a_n=a_n-1+6
  a₁=6

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)

• a_n=2+6n

• a_n=-6+6n

• a_n=6n-4

• a_n=4-6n

Find the explicit formula:
-3, -33, -63, -93, ...

• a_n = -3 - 30(n -1)

• a_n = -3 + 30(n -1)

• a_n = -30 - 3(n -1)

• a_n = -30 + 3(n -1)

Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)

• a_n = 4n + 29

• a_n = -4n + 25

• a_n = -4n + 29

• a_n = 4n + 25

Find the explicit formula:
-23, -16, -9, -2, ...

• a_n = -23 + 7(n -1)

• a_n = -23 - 7(n -1)

• a_n = 7 - 23(n -1)

• a_n = 7 + 23(n -1)

Is the sequence arithmetic: 37, 31, 25, 19, ...

• Yes

• No

• The initial term in a sequence (the first number)

• The number we are multiplying one term by to get to the next term 

• the common difference