Final answer:
The student is asked to evaluate S₅ for the sequence 400 + 200 + 100 + ..., which is a geometric series. The sum S₅ is 775, by applying the formula for the sum of the first n terms of a geometric sequence. The correct answer is thus option b. 0775.
Step-by-step explanation:
The student is asking to evaluate S₅ for the arithmetic sequence 400 + 200 + 100 + .... Since S₅ represents the sum of the first five terms, we can direct our attention to identifying the common ratio and using the formula for the sum of the first n terms of a geometric sequence. The sequence is a geometric sequence where each term is half the previous term (a common ratio of 1/2). The formula for the sum of the first n terms of a geometric sequence is S₅ = a (1 - r^n) / (1 - r), where a is the first term and r is the common ratio.
Thus, S₅ for this sequence is S₅ = 400 (1 - (1/2)^5) / (1 - 1/2) = 400 (1 - 1/32) / (1/2) = 400 (31/32) * 2 = 775. Therefore, the correct answer is 775, which is option b. 0775.