Patterns & Sequences in Generational Wealth Transfer Vocabulary Review

How to Use

• Review each term and example before your quiz.
• Read the math, real-life, and fairness examples to see how arithmetic patterns connect to wealth and opportunity.
• Keep this sheet in your Equity in Numbers Student Journal for use alongside your video and journal prompts.
• Remember: Patterns tell stories — and math helps us understand who has access to opportunity and how fairness can grow.

Pattern

• Definition: A repeated or predictable relationship between numbers or objects.
• Math Examples:
  • 2, 4, 6, 8, … (adds +2 each time)
  • 10,000 → 15,000 → 20,000 → 25,000 → …
• Real-Life Example: A family increases savings by $5,000 each generation.
• Fairness Example: Patterns reveal how wealth grows steadily for some families — and more slowly for others — showing where opportunity gaps begin.

Sequence

• Definition: A list of numbers arranged in a specific order that follows a pattern or rule.
• Math Examples:
  • 5, 10, 15, 20, …
  • 20,000 → 40,000 → 60,000 → 80,000 → …
• Real-Life Example: Generations in a family passing down wealth every 20 years.
• Fairness Example: Comparing two sequences helps us see which families’ wealth increases faster — and how that affects fairness over time.

Arithmetic Sequence

• Definition: A sequence where the same number (the common difference) is added to each term to get the next.
• Math Examples:
  • (a₁ = 10,000,\ d = 5,000) → 10,000, 15,000, 20,000, 25,000
  • Formula: (aₙ = a₁ + (n – 1)d)
• Real-Life Example: Each generation adds the same amount to their savings.
• Fairness Example: Arithmetic sequences model steady, predictable growth — but when different families start with different first terms, gaps widen over time.

Term (aₙ)

• Definition: Each number in a sequence.
• Math Examples:
  • In 2, 4, 6, 8 → 6 is the 3rd term ((a₃ = 6)).
  • In 10,000 → 15,000 → 20,000 → 25,000 → (a₄ = 25,000).
• Real-Life Example: Each term could represent a new generation’s total wealth.
• Fairness Example: Comparing later terms shows how small starting differences create large wealth gaps over generations.

First Term (a₁)

• Definition: The first number in a sequence — the starting value.
• Math Examples:
  • (a₁ = 5,000) in 5,000, 10,000, 15,000, …
• Real-Life Example: The amount of wealth or property a family begins with.
• Fairness Example: A higher starting term gives some families a head start — showing how generational privilege can continue to grow.

Common Difference (d)

• Definition: The fixed amount added to each term in an arithmetic sequence.
• Math Examples:
  • For 10,000 → 15,000 → 20,000 → 25,000 → (d = 5,000).
  • Formula: (aₙ = a₁ + (n – 1)d).
• Real-Life Example: Each generation adds $5,000 to family savings.
• Fairness Example: Families with larger common differences (more added each generation) gain wealth faster, widening the opportunity gap.

Formula for Arithmetic Sequence

• Definition: A rule that finds any term in a sequence using the first term and common difference.
• Math Example: (aₙ = a₁ + (n – 1)d)
  • Example: (a₄ = 10,000 + (4 – 1)(5,000) = 25,000)
• Real-Life Example: Predicting how much wealth a family will have after four generations.
• Fairness Example: The formula shows how math can make invisible inequality measurable — turning stories of unfairness into numbers we can analyze.

Increase / Growth

• Definition: When a number or value rises by a set amount over time.
• Math Examples:
  • 2,000 → 4,000 → 6,000 → 8,000 → (+2,000 each time).
• Real-Life Example: A family’s home value increases by $20,000 each generation.
• Fairness Example: Tracking growth helps communities see who’s gaining wealth — and who needs fairer opportunities to build assets.

Generational Wealth

• Definition: Assets, money, or property passed from one generation to the next.
• Math Examples:
  • Family A’s wealth pattern: 20,000, 40,000, 60,000, 80,000 → adds $20,000 each generation.
• Real-Life Example: Parents passing down homes, savings, or investments.
• Fairness Example: Families without assets can’t create the same wealth pattern, showing how inequity can persist over time.

Equity

• Definition: Fairness that ensures everyone has the resources they need to succeed — not just equal amounts, but equal opportunity.
• Math Examples:
  • If one family’s sequence starts lower, increasing its common difference (d) helps reach fairness over generations.
• Real-Life Example: Creating programs that help families build savings or buy homes.
• Fairness Example: Equity helps close the gap between different sequences of generational wealth.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Pattern & Sequence	Predictable growth over time	Shows steady vs. unequal progress
Common Difference (d)	Constant rate of change	Measures opportunity growth
First Term (a₁)	Starting value	Reflects head start or lack of one
Generational Wealth	Wealth passed across terms	Explains long-term inequality
Equity	Adjusts growth rates	Promotes fairness over generations