To find the sum of this arithmetic series, we first need to find the common difference between each term.

The common difference is the difference between each term in the series. In this case, the common difference is 3/70 - 3/28 = 3/70 - 15/70 = -12/70 = -6/35.

Next, we need to find the number of terms in the series. To do this, we can find the nth term of the series and set it equal to the last term in the series, which is 3/550.

The nth term of an arithmetic series can be found using the formula: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.

Using this formula, we can set a_n = 3/550, a_1 = 3/28, and d = -6/35:

3/550 = 3/28 + (n-1)(-6/35)

Multiplying through by 35 to clear the denominators:

3/10 = 15/28 - 6n + 6

3/10 = 15/28 - 6n + 6

3/10 - 15/28 = -6n + 6

84/280 - 150/280 = -6n + 6

-66/280 = -6n + 6

-33/140 = -6n + 6

-33 = -6n + 840

-873 = -6n

n = 145.5

Since we can't have a fraction of a term, we will round down to the nearest whole number, so there are 145 terms in the series.

Now, we can use the formula for the sum of an arithmetic series to find the total sum:

S_n = n/2 * (a_1 + a_n)

S_145 = 145/2 * (3/28 + 3/550)

S_145 = 72.5 * (3/28 + 3/550)

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