Question 4
In Pascal’s Triangle, each entry is the sum of the two entries above it. The first few rows of the triangle are shown below.
$$
\begin{array}{rl}0:&1\\1:&1\quad1\\2:&1\quad2\quad1\\3:&1\quad3\quad3\quad1\\4:&1\quad4\quad6\quad4\quad1\\5:&1\quad5\quad10\quad10\quad5\quad1\\6:&1\quad6\quad15\quad20\quad15\quad6\quad1\end{array}
$$
In which row of Pascal’s Triangle do three consecutive entries occur that are in the ratio $3:4:5?$
$$
\begin{array}{rl}0:&1\\1:&1\quad1\\2:&1\quad2\quad1\\3:&1\quad3\quad3\quad1\\4:&1\quad4\quad6\quad4\quad1\\5:&1\quad5\quad10\quad10\quad5\quad1\\6:&1\quad6\quad15\quad20\quad15\quad6\quad1\end{array}
$$
In which row of Pascal’s Triangle do three consecutive entries occur that are in the ratio $3:4:5?$