ATLASBetaSearch subjects

Subjects

Ancient HistoryComing soon

Biology Business Studies

ChemistryComing soon

EngineeringComing soon

English Advanced English Ext 1 English Standard

English StudiesComing soon

Enterprise ComputingComing soon

Health & MovementComing soon

Legal Studies Maths Advanced Mathematics Ext 1 Mathematics Ext 2

Maths Standard 1Coming soon

Maths Standard 2Coming soon

Modern HistoryComing soon

Physics Religion I Religion II

Visual ArtsComing soon

Save your favourites

Accounts and progress tracking are coming later.

Coming later

2021 Mathematics Extension 2 Q15 (i) | HSC Atlas

← Back to Mathematics Extension 2 questions

2021HSCShort answer

Q15 (i)

2 marks

Question

Show that the triangular numbers $t_1,t_3,t_5$ , and so on, are also hexagonal numbers.

Try the question before revealing the answer.

Solution

For odd indices, let $n=2k-1$ . Then $t_{2k-1}=k(2k-1)=2k^2-k=h_k$ , so each such triangular number is hexagonal.

AI HSC Engine generated solution · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

Source

2021 HSC Mathematics Extension 2.NESAQuestion paper page 13View original source ↗

Spot a problem? Send feedback

WebsiteWhat needs attention?Tell us what looks wrong

Please do not include your name, school, or other personal details.