Final answer:
The sum of the series S145 is determined by finding the 145th term of an arithmetic sequence, which yields a value of 1444 for the 145th term. However, since this number does not match any of the provided options, there seems to be an error in the question.
Step-by-step explanation:
To evaluate the sum of the series S145 which is defined as 4+14+24+34+44+__, we first need to recognize the pattern. Each term in the series increases by 10, starting from 4.
So, to find the 145th term (a145), we use the formula for an arithmetic sequence:
an = a1 + (n - 1)d
Where a1 is the first term (which is 4 in this case), n is the term number (145), and d is the common difference between terms (10).
a145 = 4 + (145 - 1) × 10 = 4 + 144 × 10 = 4 + 1440 = 1444
Therefore, the 145th term of the series, a145, is 1444. Given the options, none of them matches a145; hence, there might have been a mistake in the provided options.