Final answer:
The sum of the first 33 terms of the arithmetic series starting with 2, 8, 14 is 3234, to the nearest integer. This result is calculated using the formula for the sum of an arithmetic series.
Step-by-step explanation:
The student is asking for the sum of the first 33 terms of the arithmetic series that starts with 2, 8, 14. To find this, we first need to determine the common difference of the sequence, and then we can apply the formula for the sum of an arithmetic series. The common difference d is the difference between any two successive terms, which in this case is 8 - 2 = 6.
The formula for the sum S of the first n terms of an arithmetic series is S = n/2 * (2a + (n - 1)d), where a is the first term and n is the number of terms. Substituting into this formula, we get S = 33/2 * (2*2 + (33 - 1)*6),
which simplifies to S = 16.5 * (4 + 192)
= 16.5 * 196
= 3234.
Therefore, the sum of the first 33 terms of the series, to the nearest integer, is 3234.