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Odd Borders Build the Square Numbers

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Predicting What Comes Next: Exploring Sequences and Progressions · Sequences and their notation · 3:38

You'll learn: Connect successive odd additions with enlarging square arrays.

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Odd Borders Build the Square Numbers

3:38

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Odd Borders Build the Square Numbers

You'll learn: Connect successive odd additions with enlarging square arrays.

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Same topic

Sequences and their notation

4

A Sequence Is an Ordered List of Terms
3:48
A Sequence Is an Ordered List of Terms
You'll learn: Explain position, term value, ellipsis and finite versus infinite sequences.
Build Triangular Numbers by Adding the Next Row
3:35
Build Triangular Numbers by Adding the Next Row
You'll learn: Connect dot arrays with cumulative sums of natural numbers.
A New Sequence Can Come from Running Totals
3:50
A New Sequence Can Come from Running Totals
You'll learn: Generate partial sums and compare them with the original terms.
Read Subscripts and Include Negative or Fractional Terms
3:45
Read Subscripts and Include Negative or Fractional Terms
You'll learn: Use tₙ, sₙ, uₙ and identify increasing, decreasing or signed sequences.

Next topic

Explicit and recursive rules

8

An Explicit Rule Finds a Term Directly from Its Position
3:36
An Explicit Rule Finds a Term Directly from Its Position
You'll learn: Substitute a positive integer index into a term formula.
Work Backwards to Find a Term’s Position
3:41
Work Backwards to Find a Term’s Position
You'll learn: Solve a term equation and test whether the index is a positive integer.
Generate Sequences from Linear and Quadratic Rules
3:50
Generate Sequences from Linear and Quadratic Rules
You'll learn: Evaluate several explicit rules and compare the resulting sequences.
A Recursive Rule Needs a Starting Value
3:40
A Recursive Rule Needs a Starting Value
You'll learn: Generate terms from the preceding term and compare with an explicit description.
Use a Recursive Machine That Doubles and Adds Three
3:43
Use a Recursive Machine That Doubles and Adds Three
You'll learn: Calculate successive terms and check a proposed value by continuing the rule.
A Recursive Rule Can Grow Much Faster Than Addition
3:41
A Recursive Rule Can Grow Much Faster Than Addition
You'll learn: Evaluate a rule that multiplies the previous term by one less than itself.
The Next Virahanka–Fibonacci Term Uses the Previous Two
3:46
The Next Virahanka–Fibonacci Term Uses the Previous Two
You'll learn: Generate the sequence from two initial values and explain why both are needed.
A Rule Can Use the Previous Three Terms
3:46
A Rule Can Use the Previous Three Terms
You'll learn: Apply a three-term recurrence and contrast its initial conditions with the two-term rule.

Next topic

Arithmetic progressions

3

Recognise an Arithmetic Progression by Its Constant Difference
3:50
Recognise an Arithmetic Progression by Its Constant Difference
You'll learn: Compare successive differences and identify the special class of sequences.
Why an AP’s nth Term Uses n−1 Steps
3:35
Why an AP’s nth Term Uses n−1 Steps
You'll learn: Count the jumps from the first term to derive tₙ=a+(n−1)d.
APs Can Decrease or Have Fractional Terms
3:43
APs Can Decrease or Have Fractional Terms
You'll learn: Identify a and d in positive, negative, fractional and decimal examples.