Question

Determine the row and column which 100 occur.

$\left[\begin{array}{cccccc}1& 3& 6& 10& 15& \dots \\ 2& 5& 9& 14& 20& \dots \\ 4& 8& 13& 19& 26& \dots \\ 7& 12& 18& 25& 33& \dots \\ 11& 17& 24& 32& 41& \dots \\ 16& 23& 31& 40& 50& \dots \\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\end{array}\right]$

Short answer

The number 100 occur in seventh row and eighth column.

Step-by-step solution

– Given information.

The matrix,

$\left[\begin{array}{cccccc}1& 3& 6& 10& 15& \dots \\ 2& 5& 9& 14& 20& \dots \\ 4& 8& 13& 19& 26& \dots \\ 7& 12& 18& 25& 33& \dots \\ 11& 17& 24& 32& 41& \dots \\ 16& 23& 31& 40& 50& \dots \\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\end{array}\right]$

– Name the row.

Use the pattern of numbers, the row of 100 is seven.

– Name the column.

Use the pattern of numbers, the column of 100 is eight.