Tunnel Vision?
A highway tunnel is being constructed with a series of identical sections. Each section is 15 meters long and has an entrance and an exit. If the total length of the tunnel is 1.5 kilometers, calculate the number of sections and find the sum of the distances between the entrance and exit of all sections. Consider the entrance of the first section as the reference point.
1 Answer
📌 CONCEPT: A sequence is a set of numbers in a specific order, and a series is the sum of a sequence.
📐 RULE / FORMULA: The formula for the sum of an infinite geometric series is S = a / (1 - r), where a is the first term and r is the common ratio.
💡 WORKED EXAMPLE: Consider a geometric series with first term a = 2 and common ratio r = 1/2. To find the sum, we use the formula S = a / (1 - r) = 2 / (1 - 1/2) = 4.
⚠️ COMMON MISTAKE: Students often confuse the formula for the sum of an infinite geometric series with the formula for the sum of a finite series, or they fail to check if the series is geometric before applying the formula.
31 Jul 26
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