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