Arithmetic Sequence: Recursive

Define arithmetic sequences.

• A sequence whose terms change by adding the same number each time.

• A sequence whose terms change by multiplying the same number each time.

• A sequence whose terms change by dividing the same number each time.

• A list of numbers that often (but not always) form a pattern.

Define common difference.

• the product between two consecutive terms of a geometric sequence.

• the product between two consecutive terms of an arithmetic sequence.

• the difference between two consecutive terms of an arithmetic sequence.

• the difference between two consecutive terms of a geometric sequence.

A formula that requires the computation of all previous terms to find the value of a_n.

• Explicit Formula

• Recursive Formula

• Arithmetic Formula

• Geometric Formula

Which formula is used to find the recursive equation for arithmetic sequences?

• a_n = a_n-1 + d

• a_n = a_n-1 * r

• a_n = a₁ + d(n-1)

• a_n = a₁ * r^n-1

Which formula, written in words, represents the recursive rule for an arithmetic sequence?

• "previous term" plus the "common difference"

• "start value" plus the "common difference" multiplied by the "variable"

• "start value" multiplied by the "common ratio" to the power of the "variable"

• "previous term" multiplied by the "common ratio"

What is an arithmetic sequence?

A sequence made by ______ the ____ value each time.

• adding; first

• multiplying; same

• adding; same

• multiplying; first

The recursive formula is used to find the next value in a sequence of numbers.

• True
• False

The difference between two terms

in an arithmetic sequence

is called a ​ ​ (a)   ​

• Common Difference
• Formula
• Common Ratio
• Common Factor

Tags

A.FGR.2.1

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

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1