What is the sum of the odd integers from 11 through 39, inclusive?
We want to sum the arithmetic series $11 + 13 + \cdots + 39$, which has common difference 2. Suppose the series has $n$ terms. 39 is the $n$th term, so $39 = 11 + (n-1)\cdot2$. Solving, we get $n = 15$.The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $(11 + 39)/2 \cdot 15 = \boxed{375}$.
375
Level 4
Algebra
Problem: What is the sum of the odd integers from 11 through 39, inclusive?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the sum of the odd integers from 11 to 39, we first identify the sequence of odd integers within this range. The odd integers starting from 11 are 11, 13, 15, ..., up to 39. 

Next, we determine the first term (a) and the last term (l) of this arithmetic sequence. Here, a = 11 and l = 39. 

We also need to find the number of terms (n) in this sequence. The general formula for the nth term of an arithmetic sequence is given by:
l = a + (n - 1)d, where d is the common difference. For odd integers, d = 2.

Setting up the equation:
39 = 11 + (n - 1) * 2.

Rearranging gives:
39 - 11 = (n - 1) * 2,
28 = (n - 1) * 2,
n - 1 = 14,
n = 15.

Thus, there are 15 terms in this sequence.

To find the sum (S) of an arithmetic series, we can use the formula:
S = n/2 * (a + l).

Substituting the known values:
S = 15/2 * (11 + 39),
S = 15/2 * 50,
S = 15 * 25,
S = 375.

Therefore, the final answer is 375.<|END_OF_LATENT|> The final answer is $375$.