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When Does a Natural-Number Sum First Exceed One Thousand?

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Predicting What Comes Next: Exploring Sequences and Progressions · Chapter challenge problems · 3:51

You'll learn: Use the triangular-sum formula and test neighbouring integer positions.

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When Does a Natural-Number Sum First Exceed One Thousand?

3:51

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When Does a Natural-Number Sum First Exceed One Thousand?

You'll learn: Use the triangular-sum formula and test neighbouring integer positions.

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Chapter challenge problems

11

A Shifted Recursive Sequence Can Reveal a GP
3:28
A Shifted Recursive Sequence Can Reveal a GP
You'll learn: Transform the recurrence into a geometric rule and identify a target term.
Count Multiples Within a Fixed Number Range
3:46
Count Multiples Within a Fixed Number Range
You'll learn: Use the smallest and largest allowable multiples and the AP term formula.
Recover an AP from Sums of Two Terms
3:41
Recover an AP from Sums of Two Terms
You'll learn: Convert term-sum information into two linear conditions on a and d.
Write One Hundred as Consecutive Natural Numbers
3:37
Write One Hundred as Consecutive Natural Numbers
You'll learn: Use a starting value and number ofterms to find every valid representation.
A Doubling Bacterial Culture Uses Stage Zero
3:43
A Doubling Bacterial Culture Uses Stage Zero
You'll learn: Model the initial count and subsequent hourly doublings.
Find a GP from an Initial Sum and Later-Term Relation
3:49
Find a GP from an Initial Sum and Later-Term Relation
You'll learn: Express the two conditions using a and r and find possible progressions.
Find Three GP Terms from Their Sum and Product
3:51
Find Three GP Terms from Their Sum and Product
You'll learn: Use the middle term and equal ratios to constrain the first and third terms.
Equally Spaced GP Positions Also Form a GP
3:33
Equally Spaced GP Positions Also Form a GP
You'll learn: Compare the ratios between terms separated by the same number of steps.
Recover Three GP Terms from a Sum and Sum ofSquares
3:39
Recover Three GP Terms from a Sum and Sum ofSquares
You'll learn: Combine algebraic identities with the GP middle-term relation.
A Sum-Based Recurrence Can Collapse to Doubling
3:38
A Sum-Based Recurrence Can Collapse to Doubling
You'll learn: Subtract consecutive recurrence statements to simplify the rule.
Find a Familiar Sequence Hidden in Another Recurrence
3:44
Find a Familiar Sequence Hidden in Another Recurrence
You'll learn: Compare consecutive cumulative-sum rules and recognise a two-term recurrence.