Matchstick Patterns

Observe the dot patterns shown.

Generalise and find out how many dots the $n^{th}$ arrangement will contain.

Observe the dot patterns shown.

Generalise and find out how many dots the $n^{th}$ arrangement will contain.

Study the matchstick patterns shown in figure,

Write down the pattern using numbers

Study the matchstick patterns shown in figure,

Write down the pattern using numbers

.

Write the general formula for the following pattern of houses made from matchsticks and hence deduce the number of matchsticks required to make $7$ such houses:

Look at the matchstick pattern given below for letter $\mathrm{N}$:

Generalise a rule for the number of matchsticks required for making $x$ number of $\mathrm{N}$s. Also find out how many matchsticks are required for making $12 \mathrm{N}$s.

Study the matchstick patterns shown in the figures below:

If the sum of the expressions for the number of matchsticks in the $n^{\text{th }}$ shape of both patterns is of the form $ax+b$, then find the value of $a+b$. 

Study the matchstick patterns in the given figures.

Write down the rule to go from one shape to the next.

Observe the dot patterns shown in figures below. For each pattern,

Write down the pattern using numbers and the rule to go from one arrangement to the next.