Arithmetic Sequences Explicit and Recursive and Linear Equations

A sequence in which the difference between consecutive terms is constant.

• Arithmetic Sequence

• Geometric Sequence

• Infinite Sequence

A formula that directly calculates the value of a specific term in a sequence without needing information about previous terms.

• Recursive Formula

• Explicit Formula

Fill in the blanks to complete the sequence: If the first two terms of an arithmetic sequence are 2 and 4 what would the next two numbers be? Sequence: 2, 4, ______ , ______

• 8, 16

• 6, 8

• 16, 256

• 2, 4

Answer explanation

Arithmetic sequence means a sequence where you ADD the same thing over and over. AKA linear sequence

Write the explicit rule for this tile pattern.

• f(n)= 2n + 3

• f(n) = 3n + 2

• f(n) = 3n + 3

• f(n) = 2n + 2

Write the recursive rule for this tile pattern.

• next=previous + 2

• previous = next + 2

• next = 2(previous)

• y=2x+3

Which of the following are explicit equations? Choose all that apply.

• A

• B

• C

• D

• E

Which of the following represent linear patterns? Choose all that apply.

• A

• B

• C

• D

• E

Which of the following represent arithmetic growth? Choose all that apply.

• A

• B

• C

• D

• E

What would be the recursive equation for the sequence?

• next = previous + 8

• next = 3 (previous)

• next = previous + 3

• previous = 3 (next)

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)