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The question asks to write the arithmetic series given in sigma notation, and the series is:

\[
8 + 16 + 24 + 32 + \ldots + 75
\]

Now, let's find the correct sigma notation representation. The series is arithmetic with the following characteristics:

1. First term \( a = 8 \)
2. Common difference \( d = 8 \)
3. The last term is \( 75 \)

The general form of an arithmetic sequence is:

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

To find the total number of terms \( n \), use the equation for the \(n\)-th term:

\[
75 = 8 + (n - 1) \cdot 8
\]

Solving for \( n \):

\[
75 - 8 = (n - 1) \cdot 8 \\
67 = (n - 1) \cdot 8 \\
n - 1 = \frac{67}{8} = 8.375 \quad \text{(invalid)} 
\]

It seems I made a mistake in interpreting the terms. Let me correct it.



Write the following arithmetic series in sigma notation: 8 + 16 + 24 + ... + 75

Learn how to express the arithmetic series 8 + 16 + 24 + ... + 75 in sigma notation. This detailed solution covers key mathematical concepts such as arithmetic sequences, sigma notation, and series. Suitable for students in Grades 9-12.

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