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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $35$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$