A series of books was published at ten-year intervals. When the 10th book was…
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A series of books was published at ten-year intervals. When the 10th book was issued, the sum of the publication years was 19,560. When was the first book published?
Answer: A. 1911 — Concept: When quantities occur at fixed intervals (like publication years spaced by a constant number of years), they form an arithmetic progression (AP). For…
- A.
1911
- B.
1910
- C.
1914
- D.
1909
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Correct answer: A
Concept: When quantities occur at fixed intervals (like publication years spaced by a constant number of years), they form an arithmetic progression (AP). For an AP with first term a and common difference d, the sum of n terms equals n·a + d·[0 + 1 + 2 + ... + (n-1)].
Let the first publication year be x. Since the books appear at ten-year intervals and 10 books were published, the years are x, x+10, x+20, ..., x+90 — an AP with 10 terms and common difference 10.
Sum of the 10 years = 10x + (0+10+20+...+90).
Set this equal to the given total: 10x + (0+10+20+...+90) = 19,560.
Solving the resulting linear equation for x gives x = 1911.
Cross-check: Listing the ten years starting from 1911 and spaced 10 years apart, and adding them together, reproduces the given total of 19,560 exactly — confirming the first book was published in 1911.