Question

match the vocabulary word with the definition.
a sequence that increases or decreases by a constant value
a set of numbers in a specific order
constant value in an arithmetic sequence
used to determine the next term of a sequence from one or more of the preceding terms
each number in a sequence
used to determine any specific term in a sequence
arithmetic sequence sequence common difference recursive form term explicit formula

Explanation:

To solve this vocabulary matching problem, we analyze each definition and match it with the correct term:

1. "a sequence that increases or decreases by a constant value" → This is the definition of an Arithmetic Sequence (since arithmetic sequences have a common difference, a constant value added/subtracted).
2. "a set of numbers in a specific order" → This is the definition of a Sequence (a sequence is simply an ordered list of numbers).
3. "constant value in an arithmetic sequence" → This is the Common Difference (the constant value that defines the change between terms in an arithmetic sequence).
4. "used to determine the next term of a sequence from one or more of the preceding terms" → This is the Recursive Formula (recursive formulas use previous terms to find the next term).
5. "each number in a sequence" → This is a Term (each individual element in a sequence is called a term).
6. "used to determine any specific term in a sequence" → This is the Explicit Formula (explicit formulas allow you to calculate any term directly, without needing previous terms).

Final Matches:

• a sequence that increases or decreases by a constant value → Arithmetic Sequence
• a set of numbers in a specific order → Sequence
• constant value in an arithmetic sequence → Common Difference
• used to determine the next term of a sequence from one or more of the preceding terms → Recursive Formula
• each number in a sequence → Term
• used to determine any specific term in a sequence → Explicit Formula

Answer:

To solve this vocabulary matching problem, we analyze each definition and match it with the correct term:

1. "a sequence that increases or decreases by a constant value" → This is the definition of an Arithmetic Sequence (since arithmetic sequences have a common difference, a constant value added/subtracted).
2. "a set of numbers in a specific order" → This is the definition of a Sequence (a sequence is simply an ordered list of numbers).
3. "constant value in an arithmetic sequence" → This is the Common Difference (the constant value that defines the change between terms in an arithmetic sequence).
4. "used to determine the next term of a sequence from one or more of the preceding terms" → This is the Recursive Formula (recursive formulas use previous terms to find the next term).
5. "each number in a sequence" → This is a Term (each individual element in a sequence is called a term).
6. "used to determine any specific term in a sequence" → This is the Explicit Formula (explicit formulas allow you to calculate any term directly, without needing previous terms).

Final Matches:

• a sequence that increases or decreases by a constant value → Arithmetic Sequence
• a set of numbers in a specific order → Sequence
• constant value in an arithmetic sequence → Common Difference
• used to determine the next term of a sequence from one or more of the preceding terms → Recursive Formula
• each number in a sequence → Term
• used to determine any specific term in a sequence → Explicit Formula