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OlympiadBench / 2257 / The Sieve of Sundaram uses the following infinite table of positive integers:

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Numerical

is multiple answer

false

language

English

question

The Sieve of Sundaram uses the following infinite table of positive integers: | 4 | 7 | 10 | 13 |

\cdots

| | :---: | :---: | :---: | :---: | :---: | | 7 | 12 | 17 | 22 |

\cdots

| | 10 | 17 | 24 | 31 |

\cdots

| | 13 | 22 | 31 | 40 |

\cdots

| |

\vdots

\vdots

\vdots

\vdots

| | The numbers in each row in the table form an arithmetic sequence. The numbers in each column in the table form an arithmetic sequence. The first four entries in each of the first four rows and columns are shown. Determine the number in the 50th row and 40th column.

Plain-text mathematical notation (without MathML)

The Sieve of Sundaram uses the following infinite table of positive integers:

| 4 | 7 | 10 | 13 | ⋯ |
| :---: | :---: | :---: | :---: | :---: |
| 7 | 12 | 17 | 22 | ⋯ |
| 10 | 17 | 24 | 31 | ⋯ |
| 13 | 22 | 31 | 40 | ⋯ |
| ⋮ | ⋮ | ⋮ | ⋮ |  |

The numbers in each row in the table form an arithmetic sequence. The numbers in each column in the table form an arithmetic sequence. The first four entries in each of the first four rows and columns are shown.
Determine the number in the 50th row and 40th column.

Original LaTeX notation

The Sieve of Sundaram uses the following infinite table of positive integers:

| 4 | 7 | 10 | 13 | $\cdots$ |
| :---: | :---: | :---: | :---: | :---: |
| 7 | 12 | 17 | 22 | $\cdots$ |
| 10 | 17 | 24 | 31 | $\cdots$ |
| 13 | 22 | 31 | 40 | $\cdots$ |
| $\vdots$ | $\vdots$ | $\vdots$ | $\vdots$ |  |

The numbers in each row in the table form an arithmetic sequence. The numbers in each column in the table form an arithmetic sequence. The first four entries in each of the first four rows and columns are shown.
Determine the number in the 50th row and 40th column.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2257
task_id: 5b09a2f9-a57e-584c-b8d9-ef237d39f05b
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2257
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import