Tables and Patterns

Learn arithmetic patterns, input-output tables.

Lesson 2 of 32 parts Practice Flashcards

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Arithmetic Patterns

Objective: Explain arithmetic patterns, apply the stated method, and check its conditions.

An arithmetic sequence changes by a constant difference d. With first term a₁, term n is a₁+(n−1)d because only n−1 transitions occur after the starting term. A finite observed pattern suggests a rule but does not uniquely prove it. Distinguish the term number from the number of changes after term one.

Formulas

$aₙ=a₁+(n−1)d$

Worked examples

Try itThe sequence starts at 7 and adds 6 each step. Find term 7, counting the starting term as term 1.Show answer

Step 1: Term 7 is 6 steps after the first. Step 2: Calculate 7+6(6). Step 3: The term is 43.

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Arithmetic Patterns

Objective: Explain arithmetic patterns, apply the stated method, and check its conditions.

Formulas

$aₙ=a₁+(n−1)d$

Worked examples

Try itThe sequence starts at 7 and adds 6 each step. Find term 7, counting the starting term as term 1.Show answer

Step 1: Term 7 is 6 steps after the first. Step 2: Calculate 7+6(6). Step 3: The term is 43.

Input-Output Tables

Objective: Explain input-output tables, apply the stated method, and check its conditions.

A table records paired inputs and outputs. For a stated function rule, substitute each input consistently to complete its row. A table of finitely many values can support a model but does not uniquely determine every unseen value without additional assumptions. Use the stated rule rather than guessing from only one row.

Formulas

$For y=ax+b, row x=c has y=ac+b$

Worked examples

Try itA table follows y=6x+7. What is y for input 7?Show answer

Step 1: Use the same rule for every table row. Step 2: Substitute x=7. Step 3: y=49.

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