Number Line Problem: Find the Value at the Red Point in -5 to 15 Sequence

Q: How do I find the pattern in a number sequence?

Look at the differences between consecutive numbers. In this case: 3→7 (+4), 7→11 (+4), 11→15 (+4). The common difference is +4.

Q: Why isn't the answer -9 if I subtract 4 from -5?

Because the red point is between -5 and 3, not to the left of -5! You need to move forward in the sequence from -5, which means adding 4 to get -1.

Q: How do I know which direction to go on the number line?

Look at the position of the red point relative to the known numbers. It's clearly between -5 and 3, so you need to find what comes after -5 in the sequence.

Q: Can I check my answer without doing calculations?

Yes! Count the spaces on the number line. The red point is one unit to the right of -5, and -1 is indeed one unit right of -5 on any number line.

Q: What if the pattern was different, like +3 or +5?

The same method works! Find the common difference, then apply it correctly. If it was +3: $ -5 + 3 = -2 $. If it was +5: $ -5 + 5 = 0 $.

Q: Why do we start with -5 and not another number?

Because -5 is the closest known number to the left of the red point. It's easier to move forward one step than to work backward from 3 (which would be 3 - 4 = -1).

Number Line Sequences with Pattern Recognition

What number appears at the point marked in red?

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Understand the problem

What number appears at the point marked in red?

Step-by-step solution

Let's pay attention to the numbers on the axis from left to right:

$3,7,11,15$

We'll try to find the common denominator.

Note that if we use the operation +4, we'll reach the sequence of numbers:

$3+4=7$

$7+4=11$

$11+4=15$

Therefore, the red point will be the next exercise:

$-5+4=-1$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive numbers
Technique: Apply pattern backward: from -5, subtract 4 to get -9 (wrong direction!)
Check: Verify by counting positions: -1 is exactly one position before 3 ✓

Common Mistakes

Avoid these frequent errors

Applying the pattern in the wrong direction
Don't continue the +4 pattern backward from -5 to get -9! This ignores that the red point comes AFTER -5 but BEFORE 3. Always identify the correct position first, then apply the pattern in the right direction.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

How do I find the pattern in a number sequence?

Look at the differences between consecutive numbers. In this case: 3→7 (+4), 7→11 (+4), 11→15 (+4). The common difference is +4.

Why isn't the answer -9 if I subtract 4 from -5?

Because the red point is between -5 and 3, not to the left of -5! You need to move forward in the sequence from -5, which means adding 4 to get -1.

How do I know which direction to go on the number line?

Look at the position of the red point relative to the known numbers. It's clearly between -5 and 3, so you need to find what comes after -5 in the sequence.

Can I check my answer without doing calculations?

Yes! Count the spaces on the number line. The red point is one unit to the right of -5, and -1 is indeed one unit right of -5 on any number line.

What if the pattern was different, like +3 or +5?

The same method works! Find the common difference, then apply it correctly. If it was +3: $-5 + 3 = -2$ . If it was +5: $-5 + 5 = 0$ .

Why do we start with -5 and not another number?

Because -5 is the closest known number to the left of the red point. It's easier to move forward one step than to work backward from 3 (which would be 3 - 4 = -1).

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