Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence/Examples

Examples of Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence

The first instances of rows of Pascal's triangle which contain $3$ integers in arithmetic sequence are as follows:

$7, 21, 35$

The integers:

$7, 21, 35$

are in arithmetic sequence and appear in row $7$ of Pascal's triangle.

$1001, 2002, 3003$

The integers:

$1001, 2002, 3003$

are in arithmetic sequence and appear in row $14$ of Pascal's triangle.

$490 \,314, 817 \, 190, 1 \, 144 \, 066$

The integers:

$490 \, 314, 817 \, 190, 1 \, 144 \, 066$

are in arithmetic sequence and appear in row $23$ of Pascal's triangle.