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Home » Boules non bleues = 5 + 2 = 7 - Imagemakers

Boules non bleues = 5 + 2 = <<5+2=7>>7 - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 $$Question: A museum curator notes that the number of artifacts displayed in each of five consecutive exhibitions forms an arithmetic sequence. If the total number of artifacts displayed over these five exhibitions is 150 and the number of artifacts in the third exhibition is twice the number in the first, find the number of artifacts in the fifth exhibition.

📌 Solution: Let the number of artifacts in the five exhibitions be $ a - 2d, a - d, a, a + d, a + 2d $, forming an arithmetic sequence with common difference $ d $. The total number of artifacts is:

📌 Were also told the third exhibition has twice the number of the first:

📌 The fifth exhibition has $ a + 2d = 30 + 2(7.5) = 45 $.

📌 Question: An entomologist studying pollination tracks the number of visits by bees to a series of five experimental crop plots. The number of visits forms a geometric sequence. If the total number of visits is 62 and the number of visits to the third plot is 6, find the common ratio of the sequence.

📌 Solution: Let the number of visits be $

📌 Since $ r > 0 $, take the positive root. Then solve $ r +

📌 The common ratio $ r $ is the positive solution to this quadratic. However, since the total sum and middle term are integers, and the sequence is geometric, we test small integer ratios. Try $ r = 2 $:

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