Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence/Examples/7, 21, 35

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

The integers:

$7, 21, 35$

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


Proof

We have:

\(\ds 21 - 7\) \(=\) \(\ds 14\)
\(\ds 35 - 21\) \(=\) \(\ds 14\)

thus demonstrating the common difference of $14$.


Then we have that row $7$ of Pascal's triangle is:

$1, \color {red} {7, 21, 35}, 35, 21, 7, 1$

$\blacksquare$


Sources