Sum of all multiples of 8 between 200 and 400 (inclusive). Compute the arithmetic progression sum.

Introduction / Context:All integers divisible by a fixed number form an AP. Summing such terms over a closed interval reduces to counting how many terms fall in range and applying the AP sum formula.

Given Data / Assumptions:

• First multiple ≥ 200: 200 (25*8).
• Last multiple ≤ 400: 400 (50*8).
• d = 8.

Concept / Approach:Find n = ((last − first)/d) + 1, then S_n = n/2 * (first + last).

Step-by-Step Solution:n = (400 − 200)/8 + 1 = 25 + 1 = 26.S = 26/2 * (200 + 400) = 13 * 600 = 7800.

Verification / Alternative check:Average term is (200+400)/2 = 300; with 26 terms, 26*300 = 7800, consistent.

Why Other Options Are Wrong:7600, 7200, 7900 correspond to miscounting n or using wrong endpoints.

Common Pitfalls:Accidentally excluding endpoints even though both are divisible by 8; using 24 or 25 terms instead of 26.

Final Answer:7800