Question

Form an algebraic expression to give the number of line segments required to make the pattern given below and find the number of line segments required for $10$ houses.

Answer 1

Step 1: Analyze the figure.

From figure, it is clear that

The first pattern requires $6$ line segments, and every additional pattern after the first requires $5$ line segments.

Step 2: Deduction the pattern.

Every pattern requires additional $5$ line segments except the first one which requires $6$ line segments.

Therefore, rule is $5n+1$, where $n$ is representing the number of house.

Step 3: Verification of pattern.

When $n=1$, we have $5n+1=6$.

When $n=2$, we have $5n+1=11$.

When $n=3$, we have $5n+1=16$.

So, the number of line segments required for $10-$house patterns is

$$\begin{gathered} =5n+1 \\ =5\times 10+1 \\ =51 \end{gathered}$$

Hence, number of line segments required for $10$ houses are $51$.