Question

Write the general algebraic expression for the pattern given below. Also, find the number of line segments required for $12$ of the given pattern.

Answer 1

Step 1: Find the number of line segments required for $12$ the given pattern.

Given

The first pattern requires $4$ line segments, and every additional pattern after the first requires $6$ line segments.

Step 2: Generalise the pattern.

Every pattern requires $6$ line segments except the first one which requires two fewer line segments.

Therefore, the rule is$6n-2$.

Step 3: Verify the pattern.

When$n=1$ we have$6n-2=4$.

When $n=2$we have $6n-2=10$

When$n=3$ we have $6n-2=16$

So, the number of line segments required for $12$ such patterns

$$\begin{gathered} =6n-2 \\ =6\times 12-2 \\ =72-2 \\ =70 \end{gathered}$$

Step 4: Final answer.

Hence, the number of line segments required is$70$.