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3. Patterns using matchsticks/Ice candy sticks

Suppose you are given with

$3$ Matchsticks and asking you to form the letter

$C$ using that. It is easy for you to form the letter

$C$ right.

Your work might be like this.

Suppose we want one more

$C$ . Then how many sticks you will need?

Yes, We need another

$3$ sticks. In total, we need

$3 + 3 = 6$ sticks.

Adding one more letter

$C$ will become:

Here we used

$3+3+3 = 9$ sticks.

Thus, to form one

$C$ we need

$3$ sticks, to form two

$C$ 's we need

$6$ sticks, to form three

$C$ 's we need

$9$ sticks, and so on.

Now tabulate the details and look for the pattern.

$C$ 's formed	$1$	$2$	$3$	$4$	$5$
Number of matchsticks needed	$3$	$6$	$9$	$12$	…

Look at the numbers of matchsticks used to form

$C$ 's.

$3, 6, 9, 12,….$

In this sequence, the next number should be

$15$ .

Because the number of matchsticks needed is three times the number of

$C$ 's formed.

Let us take the general number

$n$ for the number of matchsticks needed.

If one

$C$ is made, then

$n=1$ .

If two

$C$ 's are made, then

$n=2$ .

If three

$C$ 's are made, then

$n=3$ .

Thus, the alphabet

$n$ can be any natural number

$1, 2, 3, 4,...$ .

The number of matchsticks required for forming any number of

$C$ 's

$= 3 × n$ .

Instead of writing

$3 × n$ , we can write

$3n$ .

Let us try to get the answer from the above form.

To form one

$C$ ,

$n=1$ and the number of matchsticks required

$=3×1 =3$ .

To form two

$C$ ,

$n=2$ and the number of matchsticks required

$=3×2 =6$ .

To form three

$C$ ,

$n=3$ and the number of matchsticks required

$=3×3 =9$ .

Thus, we got the generalized rule to find the number of matchsticks required to form any number of

$C$ 's.

Is it possible to find the number of matchsticks required to form ten

$C$ 's without drawing its pattern?

Think!

Of course. It is possible.

Just by substituting

$n=10$ in the rule

$3n$ , we are able to get the number of matchsticks required to form ten

$C$ 's.

That is,

$3×10 = 30$ matchsticks required.

Now can you find the number of matchsticks required to form

$100$

$C$ 's?

Yes, we can get. Substitute

$n = 100$ in the rule

$3n$ .

That is,

$3×10 = 30$ matchsticks required.

From the above demonstration, we got the rule to find the number of matchsticks required to make a pattern of

$C$ s.

The rule is:

Number of matchsticks required = 3n

Where

$n$ is the number of

$C$ s in the pattern and

$n$ takes the values from the natural number

$1,2,3,4,...$ .

Important!

What is the variable?

In the example,

$n$ is a variable. It is not a fixed value. In the above example, the variable

$n$ can take any natural number

$1,2,,3,...$ . We can write the number of matchsticks required using the variable

$n$ .

The word 'variable' means something that can vary, i.e. change. The value of a variable is not fixed. It can take different value.

Additionally, imagine other letters of the alphabets(other than

$C$ ) that can be made from matchsticks/Ice candy sticks.

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3. Patterns using matchsticks/Ice candy sticks

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