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Recognise an Arithmetic Progression by Its Constant Difference

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Predicting What Comes Next: Exploring Sequences and Progressions · Arithmetic progressions · 3:50

You'll learn: Compare successive differences and identify the special class of sequences.

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Recognise an Arithmetic Progression by Its Constant Difference

3:50

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Recognise an Arithmetic Progression by Its Constant Difference

You'll learn: Compare successive differences and identify the special class of sequences.

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Same topic

Arithmetic progressions

4

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.
Plot an AP as Discrete Points on a Straight Line
3:56
Plot an AP as Discrete Points on a Straight Line
You'll learn: Turn a term table into ordered pairs(index, value).
Write the Same AP Explicitly and Recursively
3:48
Write the Same AP Explicitly and Recursively
You'll learn: Translate between tₙ=a+(n−1)d and tₙ=tₙ₋₁+d.

Next topic

AP applications and recovery problems

3

Find a Distant AP Term or Test Membership
3:28
Find a Distant AP Term or Test Membership
You'll learn: Use the general term forwards and backwards.
Recover an AP from Two Term Conditions
3:43
Recover an AP from Two Term Conditions
You'll learn: Use differences between term equations to find a and d.
Taxi Fares and Salaries Can Form APs
3:43
Taxi Fares and Salaries Can Form APs
You'll learn: Identify the first observed term and the fixed increment in a context.

Next topic

Sums of natural numbers and triangular numbers

4

Pair a Sum with Its Reverse
3:37
Pair a Sum with Its Reverse
You'll learn: Add1–10 in opposite directions so every column has the same total.
Derive the Sum of the First n Natural Numbers
3:36
Derive the Sum of the First n Natural Numbers
You'll learn: Generalise the reversed-sum proof and connect it to a rectangular dot array.
Find a Sum That Starts Somewhere Other Than One
3:50
Find a Sum That Starts Somewhere Other Than One
You'll learn: Subtract two initial sums to retain exactly the intended interval.
The nth Triangular Number Is a Sum
3:31
The nth Triangular Number Is a Sum
You'll learn: Connect the original triangle arrays to the closed term formula.

Next topic

Natural-number sums and AP applications

1

Count and Add the Two-Digit Multiples of Three
3:35
Count and Add the Two-Digit Multiples of Three
You'll learn: Identify the first and last terms, count the steps and add the required multiples.

Next topic

Geometric progressions

3

A GP Multiplies Where an AP Adds
3:54
A GP Multiplies Where an AP Adds
You'll learn: Compare equal differences with equal ratios using the two growth pictures.
Why a GP’s nth Term Has Exponent n−1
3:35
Why a GP’s nth Term Has Exponent n−1
You'll learn: Count repeated multiplications to derive tₙ=arⁿ⁻¹.
Find the Common Ratio in Growing and Shrinking GPs
3:42
Find the Common Ratio in Growing and Shrinking GPs
You'll learn: Divide consecutive non-zero terms and derive term formulas.