Final answer:
To find the sum of the arithmetic series 4 + 11 + 18 + 25 + ... + 1439, the number of terms (n) is determined to be 206 using the formula for the nth term of an arithmetic sequence. Then, using the sum formula for arithmetic series, the sum is calculated to be 148629.
Step-by-step explanation:
To find the sum of the arithmetic series 4 + 11 + 18 + 25 + ... + 1439, we first need to identify the number of terms in the series. The series starts with a first term (a) of 4 and increases by a common difference (d) of 7 (11 - 4 = 7). The series ends with a last term (l) of 1439. To find number of terms (n), we use the formula for the nth term of an arithmetic sequence:
l = a + (n - 1)d
Substituting the known values, we get:
1439 = 4 + (n - 1)*7
1439 = 4 + 7n - 7
1439 = 7n - 3
1439 + 3 = 7n
1442 = 7n
n = 1442 / 7
n = 206
There are 206 terms in the arithmetic series. Now, we use the sum formula for an arithmetic series, which is:
S = n/2 * (a + l)
Substituting the known values, we find the sum:
S = 206/2 * (4 + 1439)
S = 103 * 1443
S = 148629
The sum of the series is 148629.