A series of books was published at seven-year intervals. When the seventh book…
2024
A series of books was published at seven-year intervals. When the seventh book was issued, the sum of the publication years was 13,524. When was the first book published ?
- A.
1918
- B.
1915
- C.
1911
- D.
1912
Attempted by 590 students.
Show answer & explanation
Correct answer: C
Answer: 1911
Let the first publication year be x. The seven books were published at seven‑year intervals, so the years are:
x, x+7, x+14, x+21, x+28, x+35, x+42
Compute the sum. Group the x terms and the added constants: sum = 7x + (0+7+14+21+28+35+42).
Evaluate the constant sum: 0+7+14+21+28+35+42 = 147, so sum = 7x + 147.
Set this equal to the given total and solve: 7x + 147 = 13,524 ⇒ 7x = 13,377 ⇒ x = 13,377 ÷ 7 = 1,911.
Conclusion: The first book was published in 1911.
Quick check: years = 1911, 1918, 1925, 1932, 1939, 1946, 1953. Sum = 13,524.