Number Line Position: Find the Value at the Red Point Between -32 and -8

Q: How do I know if it's doubling or adding a constant?

Check the ratio between consecutive numbers: $ -4 ÷ (-2) = 2 $ and $ -8 ÷ (-4) = 2 $. Since the ratio is constant, it's multiplication, not addition!

Q: Why is the red point at -16 and not -12?

The sequence follows a geometric pattern (multiply by 2) not arithmetic (add -2). Following the pattern: $ -2, -4, -8, -16 $ where each term doubles.

Q: What if the numbers were positive instead?

The same doubling pattern would work! For example: 2, 4, 8, 16. The multiplication rule applies regardless of whether numbers are positive or negative.

Q: How can I double-check my pattern is correct?

Work backwards! If -16 is correct, then $ -16 ÷ 2 = -8 $, and $ -8 ÷ 2 = -4 $. This matches the given values perfectly.

Q: Are there other types of number line patterns?

Yes! You might see arithmetic sequences (adding/subtracting the same amount) or other geometric sequences (multiplying by 3, dividing by 2, etc.). Always check what operation connects the numbers.

Number Line Patterns with Geometric Sequences

What number appears at the point marked on the axis in red?

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Understand the problem

What number appears at the point marked on the axis in red?

Step-by-step solution

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

$-2,-4,-8,\text{?}$

We'll try to find the common denominator.

Note that if we multiply by 2, we'll get the sequence of numbers:

$-2\times2=-4$

$-4\times2=-8$

Therefore, the next operation to find the red point will be:

$-8\times2=-16$

Final Answer

16-

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the relationship between consecutive marked values
Technique: From -2 to -4 to -8, multiply by 2: $-8 \times 2 = -16$
Check: Verify pattern holds: -2, -4, -8, -16 each doubles ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying to find the pattern
Don't add the same number each time like -8 + (-4) = -12! This gives wrong results because the sequence doubles, not adds. Always look for multiplication patterns when gaps between numbers aren't equal.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

How do I know if it's doubling or adding a constant?

Check the ratio between consecutive numbers: $-4 ÷ (-2) = 2$ and $-8 ÷ (-4) = 2$ . Since the ratio is constant, it's multiplication, not addition!

Why is the red point at -16 and not -12?

The sequence follows a geometric pattern (multiply by 2) not arithmetic (add -2). Following the pattern: $-2, -4, -8, -16$ where each term doubles.

What if the numbers were positive instead?

The same doubling pattern would work! For example: 2, 4, 8, 16. The multiplication rule applies regardless of whether numbers are positive or negative.

How can I double-check my pattern is correct?

Work backwards! If -16 is correct, then $-16 ÷ 2 = -8$ , and $-8 ÷ 2 = -4$ . This matches the given values perfectly.

Are there other types of number line patterns?

Yes! You might see arithmetic sequences (adding/subtracting the same amount) or other geometric sequences (multiplying by 3, dividing by 2, etc.). Always check what operation connects the numbers.

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