The given series is an arithmetic progression (AP) where:

- First term (\(a\)) = 1
- Common difference (\(d\)) = 5
- Last term (\(l\)) = 100

The formula for the sum of an arithmetic series is:

\[
S_n = \frac{n}{2} \times (a + l)
\]

where \(n\) is the number of terms in the series.

### Step 1: Find \(n\) (the number of terms)
The formula for the \(n\)-th term of an arithmetic sequence is:

\[
l = a + (n - 1) \times d
\]

Substitute the known values:

\[
100 = 1 + (n - 1) \times 5
\]

Solving for \(n\):

\[
100 - 1 = (n - 1) \times 5
\]
\[
99 = (n - 1) \times 5
\]
\[
n - 1 = \frac{99}{5} = 19.8
\]

It seems there is an issue here because \(n\) must be an integer. This suggests that the last term isn’t exactly 100 but the largest value before 100. Let's check again, finding the largest multiple of 5 that falls within the pattern. The sequence ends at 96 because 96 is a multiple of 5.

Let me redo with that clarification.

Answer coming soon as I

Learn how to find the sum of the arithmetic progression 1 + 5 + 10 + ... up to 100. This problem covers key concepts such as arithmetic sequences, series summation, and applying the sum of an arithmetic series formula. Ideal for students in Grades 8-10.

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