To find the sum of the arithmetic series 1+4+7+10+...+25, we can use the formula for the sum of an arithmetic series:

Sn = (n/2)(a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, a1 = 1, an = 25, and we need to find the value of n.

To find n, we can use the formula for the nth term of an arithmetic series:

an = a1 + (n-1)d

where d is the common difference between terms.

In this case, d = 4 - 1 = 3.

Substituting the values into the formula:

25 = 1 + (n-1)3

Simplifying:

25 = 1 + 3n - 3

25 = 3n - 2

27 = 3n

n = 9

Now that we have the value of n, we can substitute it into the formula for the sum of the series:

Sn = (n/2)(a1 + an)

Sn = (9/2)(1 + 25)

Sn = (9/2)(26)

Sn = 9 * 13

Sn = 117

Therefore, the sum of the series 1+4+7+10+...+25 is 117.