To solve the expression \(888 - 880 + 872 - 864 + 856 - 848 + \dots + 24 - 16 + 8\), we first recognize a pattern in the sequence.

This sequence alternates between addition and subtraction of terms that decrease by 8 each time. We can group each pair of terms together:

\[
(888 - 880) + (872 - 864) + (856 - 848) + \dots + (24 - 16) + 8
\]

Each pair simplifies as follows:

\[
888 - 880 = 8, \quad 872 - 864 = 8, \quad 856 - 848 = 8, \quad \dots
\]

So each pair contributes \(8\) to the total sum.

Next, we count the number of pairs in the sequence. The sequence starts at 888 and decreases by 8 until it reaches 16 (or 24 when the last term is single). This sequence can be described by:

\[
888, 872, 856, \dots, 24
\]

To find the number of terms in this arithmetic sequence:

1. First term \(a_1 = 888\).
2. Last term \(a_n = 24\).
3. Common difference \(d = -16\).

The number of terms \(n\) in the sequence is given by:

\[
a_n = a_1 + (n-1) \cdot d
\]

Plugging in the values:

\[
24 = 888 + (n-1)(-16)
\]

\[
24 - 888 = (n-1)(-16)
\]

\[
-864 = (n-1)(-16)
\]

\[
n-1 = \frac{864}{16} = 54
\]

\[
n = 55
\]

Since each pair contributes 8, the sum is:

\[
\text{Number of pairs} \times 8 = \frac{55}{2} \times 8 = 27.5 \times 8 = 220
\]

So, the total sum is **220**.

Would you like any further details on this process or have any questions?

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Here are some related questions to deepen your understanding:

1. How would the sum change if the sequence started at a different number?
2. What happens if the sequence alternated between addition and subtraction but had a different common difference?
3. How would you handle a sequence where the pattern isn't immediately obvious?
4. Can you find the sum of a similar sequence that increases instead of decreases?
5. What if the sequence ended in a negative number? How would that affect the sum?

**Tip:** When dealing with sequences, always look for patterns and try grouping terms to simplify the problem.

Learn how to calculate the sum of the arithmetic sequence 888 - 880 + 872 - 864 + ... + 24 - 16 + 8 step-by-step. This sequence alternates between addition and subtraction with a common difference of -8. Suitable for high school students, this problem explores arithmetic sequences and series summation.

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