which number is missing in the series of numbers
Answer the question mark.

20, 18, ?, 6, -10




The given sequence is: **20, 18, ?, 6, -10**.

To find the missing number, let's first observe the pattern by calculating the differences between the numbers:

1. The difference between 20 and 18: \( 18 - 20 = -2 \).
2. Let the missing number be \( x \). The difference between 18 and \( x \) is \( x - 18 \).
3. The difference between \( x \) and 6: \( 6 - x \).
4. The difference between 6 and -10: \( -10 - 6 = -16 \).

Looking at the differences:

- The first difference is -2.
- The last difference is -16.

The differences seem to be doubling:

- If we hypothesize that the differences follow a pattern where each difference is doubled, the second difference should be \( -4 \) (as \( -2 \times 2 = -4 \)).
- The third difference could then be \( -8 \) (as \( -4 \times 2 = -8 \)).

Let's test this pattern:

1. Starting from 20:
   - \( 20 - 2 = 18 \)
   - \( 18 - 4 = 14 \) (This would be the missing number.)
   - \( 14 - 8 = 6 \)
   - \( 6 - 16 = -10 \)

Thus, the missing number is **14**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How can identifying the difference between terms help in finding missing numbers in sequences?
2. What are some common patterns in number sequences besides arithmetic and geometric?
3. How can you check if a sequence is arithmetic or follows another rule?
4. What are the applications of recognizing patterns in sequences?
5. How can you use sequences to solve real-life problems?

**Tip:** Always start by looking for a pattern in the differences between terms when solving number sequences. This often helps identify the rule governing the sequence.

Learn how to identify the missing number in the sequence 20, 18, ?, 6, -10. Understand the pattern in number sequences and practice solving problems involving sequences. Suitable for students in Grades 6-8.

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