Final answer:
The sum of the first 30 terms of the arithmetic series that begins with 5, 10, 15, etc. is calculated using the arithmetic series sum formula and is found to be 2325.
Step-by-step explanation:
The question asks to find the sum of the first 30 terms of an arithmetic series that begins with 5, 10, 15, and so on. This type of series is known as an arithmetic progression, where each term increases by a common difference - in this case, 5. The formula for finding the sum of the first n terms of an arithmetic series (Sn) is Sn = n/2 * (2a + (n - 1)d), where n is the number of terms, a is the first term, and d is the common difference between the terms.
For our series:
a = 5 (the first term),
d = 5 (the common difference),
n = 30 (the number of terms we want to sum).
Applying the formula for the sum:
Sn = 30/2 * (2*5 + (30 - 1)*5)
= 15 * (10 + 29*5)
= 15 * (10 + 145)
= 15 * 155
= 2325.
Therefore, the sum of the first 30 terms of the series, to the nearest integer, is 2325.