To solve the problem, we first recognize the sequence of numbers as an arithmetic sequence of odd numbers from 11 to 999. Here's the step-by-step breakdown:

Step 1: Identify key parameters of the sequence

• First term (a_1 = 11)
• Last term (a_n = 999)
• Common difference (d = 2) (since it’s odd numbers)

Step 2: Calculate the number of terms (n)

Using the arithmetic sequence formula:
[a_n = a_1 + (n-1)d]
[999 = 11 + (n-1) \times 2]
[n-1 = \frac{999 - 11}{2} = 494]
[n = 495]

Step 3: Compute the sum of the sequence

The sum (S_n) of an arithmetic sequence is:
[S_n = \frac{n(a_1 + a_n)}{2}]
[S_n = \frac{495(11 + 999)}{2} = \frac{495 \times 1010}{2}]
[S_n = 495 \times 505 = 249975]

Answer: (\boxed{249975})

作者声明:本文包含人工智能生成内容。