Sequences / Skips

Numbers that come one after another with equal intervals between them.
The sequence can increase and the sequence can also decrease.

Always read the sequence from left to right! Just like reading a number.
Let's see what number it starts with and what number it ends with.
If the first number is smaller than the last number - there is an increase - ascending sequence
If the first number is larger than the last number - there is a decrease - descending sequence

In order to discover a pattern, let's remember the rules we learned:
A number has ones, tens, and hundreds digits
For example -
$5712$
$2$= ones digit
$1$ = tens digit
$7$ = hundreds digit
$5$= thousands digit

When we encounter a sequence - we ask ourselves -
In which digit did the change occur? Ones/Tens/Hundreds/Thousands
When we know which digit changed, we can immediately identify the intervals between the numbers and discover the pattern - adding or subtracting...
Let's look at a sample number sequence:
$5,6,7,8,9,10$
The sequence before us is an increasing sequence -
A sequence that starts at $5$
and increases up to $10$.

There are intervals of 1 between each number $1$
Therefore we can determine that:
The pattern of the sequence is $1$.

Let's look at the following sequence:
$13,15,17,19$

Let's check - whether the sequence increasing or decreasing -
The first number is $13$
and the last number is $19$
There is an increase, therefore the sequence is increasing.

Which digit changes? The ones digit.
How much does it change by each time? $2$.
The pattern is – adding $2$

Another example:
Let's explore the following sequence -
$213,223,233,243,253$
Let's check if the sequence is increasing or decreasing
The first number is $213$
The last number is $253$
There is an increase hence the sequence is increasing.
Let's check in which digit the change occurs -
The change occurs in the tens digit
Each time $10$ is added
Therefore the pattern is - adding $10$.

Another example -
$650,550,450,350$
Let's check if the sequence is increasing or decreasing -
The first number is $650$
The last number is $350$
There is a decrease hence the sequence is decreasing.
Let's check in which digit the change occurs and examine the change -
The change occurs in the hundreds digit - each time decreasing by $100$
Therefore the pattern is - subtraction of $100$

Now let's practice!
Look at the following sequence,
Complete it and determine:
Is the sequence increasing or decreasing?
What is its pattern?
$102, \_\_\_,122,132,142$

Solution
Note –
In order to complete the sequence, we will first examine it and understand whether it is increasing or decreasing and what the pattern is.
We see that the first number in the sequence is $102$
and the last number in the sequence is $142$.
There is an increase, hence the sequence is increasing.
Now let's check from the numbers we have in which digit the change occurs – in the tens digit.
We can see that each time the number increases by $10$
Therefore- the pattern is adding $10$.
Now let's complete the sequence:
If we determined that the pattern is adding $10$, all we need to do is add $10$
to the number $102$
We obtain the following:
$102+10=112$
Let's complete the sequence:
$102, {\underline{112}}, 122,132,142$

Another exercise:
Complete the following sequence,
determine whether it is increasing or decreasing and indentify its pattern.
$130, \_\_\_, 70, \_\_\_,30,10$

Solution:
First, let's understand whether the sequence is increasing or decreasing.
The first number in the sequence is $130$
The last number is $10$
There is a decrease, therefore the sequence is decreasing.

Let's examine in which digit the change occurs - the change occurs in the tens digit.
We observe that in every 2 numbers the number decreases by $20$.
Therefore, the pattern is - subtraction of $20$.
Now that we have discovered the pattern, all we need to do is complete the sequence.
In order to determine which number comes after $110$, we subtract $20$ and obtain :
$110-20=90$
In order to determine which number comes after $70$, we subtract $20$ and obtain the following:
$70-20=50$
Let's complete the sequence:
$130, 110, {\underline {90}}, 70, {\underline {50}}, 30, 10$