In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?

(The top row of Pascal's Triangle has only a single $1$ and is the $0$th row.)
Question:
In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?

(The top row of Pascal's Triangle has only a single $1$ and is the $0$th row.)
Answer:
Let's think step by step.

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In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?

(The top row of Pascal's Triangle has only a single $1$ and is the $0$th row.)
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