Arithmetic progression of publication years: A series of 7 books was published at uniform 7-year intervals. When the seventh book was issued, the sum of the publication years of all seven books was 13,524. In which year was the first book published?

Introduction / Context:
The publication years form an arithmetic progression (AP) with common difference 7 years and 7 terms. The sum of AP terms connects the first year to the total sum. Using the compact sum formula for an AP lets us compute the first publication year directly.

Given Data / Assumptions:

• Number of books n = 7.
• Common difference d = 7 years.
• Sum of the 7 publication years S = 13,524.
• Let the first year be a; then the years are a, a+7, …, a+42.

Concept / Approach:
Sum of AP: S = n/2 * [2a + (n − 1)d]. With n = 7 and d = 7, we can simplify the sum to S = 7(a + 21). Solve for a and confirm it yields integer years consistent with the described schedule.

Step-by-Step Solution:

Verification / Alternative check:
List years: 1911, 1918, 1925, 1932, 1939, 1946, 1953. Sum them or use the average: the average year is the middle term (1932). Sum = average * 7 = 1932 * 7 = 13,524, confirming the calculation.

Why Other Options Are Wrong:
1932 is the middle term (4th book), not the first. 1917, 1925, 1942 do not align with both the 7-year spacing and the given total sum simultaneously.

Common Pitfalls:
Using the wrong AP sum formula or forgetting that with an odd number of equally spaced years, the average equals the middle term, which gives a quick cross-check.

Final Answer:
1911