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We are given an arithmetic sequence where the first term $ a = 20 $ and the common difference $ d = 8 $. We are to find the total attendance over the first 15 weeks, which means we need to calculate the sum of the first 15 terms of the sequence.
The formula for the sum of the first $ n $ terms of an arithmetic sequence is:
Question: A research engineer in precision agriculture is testing sensor units that measure soil moisture. Each unit sends a signal every 6 minutes, and the engineer wants to determine how many signals are sent in a 48-hour period by one sensor. How many signals are transmitted?
Each sensor sends a signal every 6 minutes. First, convert 48 hours into minutes:
Since the sensor sends a signal every 6 minutes, the number of signals transmitted is:
Question: A science fiction writer is designing a futuristic calendar for a planet orbiting a binary star system. The planet has a unique time cycle where a tide week consists of 7 days, and every 4th tide week forms a storm week with intensified weather. If a tide week begins on day 1, on which day number does the 10th storm week begin?
The first storm week begins on day 28. The second on day 56, the third on day 84, and so on. This forms an arithmetic sequence with first term $ a = 28 $ and common difference $ d = 28 $.
We want the day number of the 10th storm week:
The sequence is arithmetic with first term $ a = 5 $ and common difference $ d = 6 $. The total number of doses after $ n $ days is the sum of the first $ n $ terms:
We want the smallest $ n $ such that: