Question

The following figure shows a stick pattern of rhombuses. Find the general rule that gives the number of sticks in terms of the number of rhombuses.

• A. 4$n$
• B. 3$n$
• C. 3$n$ + 1
• D. 4$n$ - 1

Answer 1

The correct option is C 3$n$ + 1

Here,
We see that,
1st rhombus requires 4 sticks.
2nd rhombus requires 3 new sticks and 1 stick from the neighbor.
3rd rhombus also requires 3 new sticks and 1 stick from the neighbor and so on.

Hence,

Number of Rhombus	Number of Matchsticks
$1234...n$	$3\times 1+1=43\times 2+1=73\times 3+1=103\times 4+1=13...3\times n+1=3n+1$

Thus, the general rule for the number of sticks = 3$n$ + 1, where $n$ represents the number of rhombuses.