Final answer:
To find the sum of the first 31 terms of the series 4, 11, 18,..., you can use the formula for the sum of an arithmetic series. The sum is 3380 when rounded to the nearest integer.
Step-by-step explanation:
To find the sum of the first 31 terms of the series 4, 11, 18,..., we need to first find the formula for the nth term of the series. We can observe that the series is an arithmetic sequence with a common difference of 7.
So, the formula for the nth term is 4 + 7(n-1). Plugging in n = 31, we get 4 + 7(31-1) = 4 + 7(30) = 4 + 210 = 214.
Now, to find the sum of the first 31 terms, we can use the formula for the sum of an arithmetic series, which is Sn = (n/2)(a + l), where a is the first term, l is the last term, and n is the number of terms. Plugging in a = 4, l = 214, and n = 31, we get Sn = (31/2)(4 + 214) = 15.5(218) = 3379.
The sum of the first 31 terms of the series 4, 11, 18,... to the nearest integer is 3380.