Expressions using Letter-Numbers - Pick Patterns and Reveal Relationships

Observe the pattern of matchsticks used to form the letter 'L'. One 'L' requires $2$ sticks, two 'L's require $4$ sticks, and three 'L's require $6$ sticks. Write a general rule for the number of sticks required for $n$ 'L's.

$2n$

Since each 'L' requires $2$ matchsticks, for $n$ such shapes, the total sticks needed is $2 \times n = 2n$. Here $n$ is the variable representing the number of shapes.

Find the rule for the $n^{th}$ term of the number pattern: $3, 6, 9, 12, \dots$

$3n$

The terms are multiples of $3$. For the $1^{st}$ term ($n=1$), $3 \times 1 = 3$. For the $2^{nd}$ term ($n=2$), $3 \times 2 = 6$. Thus, the general relationship is $3n$.

Identify the terms and their coefficients in the expression $1.2ab - 2.4b + 3.6a$.

Terms: $1.2ab, -2.4b, 3.6a$. Coefficients: $1.2, -2.4, 3.6$.

Terms are the parts separated by $+$ or $-$ signs. The coefficient is the numerical multiplier of the variables in each term.

If the side of a regular hexagon is denoted by $l$, express the perimeter of the hexagon using $l$.

$6l$

A regular hexagon has $6$ equal sides. If one side is $l$, the sum of all sides is $l + l + l + l + l + l = 6l$.