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Why an AP’s nth Term Uses n−1 Steps

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Predicting What Comes Next: Exploring Sequences and Progressions · Arithmetic progressions · 3:35

You'll learn: Count the jumps from the first term to derive tₙ=a+(n−1)d.

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Why an AP’s nth Term Uses n−1 Steps

3:35

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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.

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Same topic

Arithmetic progressions

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Recognise an Arithmetic Progression by Its Constant Difference
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APs Can Decrease or Have Fractional Terms
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APs Can Decrease or Have Fractional Terms
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AP applications and recovery problems

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Find a Distant AP Term or Test Membership
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Find a Distant AP Term or Test Membership
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Recover an AP from Two Term Conditions
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Recover an AP from Two Term Conditions
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Taxi Fares and Salaries Can Form APs
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Sums of natural numbers and triangular numbers

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Pair a Sum with Its Reverse
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Pair a Sum with Its Reverse
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Derive the Sum of the First n Natural Numbers
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Find a Sum That Starts Somewhere Other Than One
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The nth Triangular Number Is a Sum
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Natural-number sums and AP applications

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Count and Add the Two-Digit Multiples of Three
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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.

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Geometric progressions

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A GP Multiplies Where an AP Adds
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A GP Multiplies Where an AP Adds
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Why a GP’s nth Term Has Exponent n−1
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Find the Common Ratio in Growing and Shrinking GPs
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Find the Common Ratio in Growing and Shrinking GPs
You'll learn: Divide consecutive non-zero terms and derive term formulas.