The given sequence is an arithmetic sequence where the first term $a = 1$ and the common difference $d = 5$.

We need to find the sum of this arithmetic sequence from 1 to 100. To do so, we'll use the formula for the sum $S_n$ of an arithmetic sequence:

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

Where:

• $n$ is the number of terms,
• $a$ is the first term,
• $l$ is the last term (100 in this case).

Step 1: Find the number of terms $n$

The general term of an arithmetic sequence is given by: $a_n = a + (n-1) \cdot d$

We know the last term $a_n = 100$, so we solve for $n$:

$100 = 1 + (n-1) \cdot 5$

$99 = (n-1) \cdot 5$

$n-1 = \frac{99}{5} = 19.8$

So, $n = 20.8 + 1 = 21$