This confirms that the patient would stop taking their medication, taking 0 pills, in the sixth week. ↑ ↑ ↑ ↑ ↑ ↑ 1 2 3 4 5 6 W e e k W e e k W e e k W e e k W e e k W e e k Thus, we solve to find the value of □ in the equationĪdding 3 □ to both sides and then dividing through by 3 giveĪs □ is the number of weeks, we can answer the question that the patient stops taking their medication in the sixth week.Īs a check of our answer, we could list the values in the sequence until we get a term of 0. To find the week in which the patient stops their medicine, we need to find the week in which □ = 0 . We substitute these values into □ = □ + ( □ − 1 ) □ to find the □th term of this sequence. As the common difference decreases each week, the difference will be a negative value, so □ = − 3. In this case, the first term is 15, so □ = 1 5 . As the number of pills decreases each week by the same number, we can consider this a decreasing arithmetic sequence.Īn arithmetic sequence of index □ has a general term of In this question, a patient has begun taking medication with 15 pills in the first week. Given that the patient should decrease the dosage by 3 pills every week, find the week in which he will stop taking the medicine completely. In the next example, we will see how the arithmetic sequence formula can be applied to a decreasing sequence.Įxample 2: Finding an Unknown Term in an Arithmetic Sequence Presented as a Word ProblemĪ doctor prescribed 15 pills for his patient to be taken in the first week. Therefore, we can give the answer that the length of time that Fady exercises for on the eighteenth day is 74 minutes. Substituting □ = 1 8 into the equation □ = 4 □ + 2 and simplifying give To find the number of minutes that Fady exercises for on the eighteenth day, we calculate the 18th term, □ . We could then use the □th term to find any specific term in the sequence. We can substitute these values into the □th term formula □ = □ + ( □ − 1 ) □ to find the general term of this sequence: The common difference is the number of minutes by which Fady increases his exercise time each day, so □ = 4. The first term in the sequence is the number of minutes Fady exercises for on the first day, so □ = 6 . Where □ is the first term and □ is the common difference. An arithmetic sequence is a sequence with a common difference between successive terms.Īn arithmetic sequence of index □ has an □th term of We notice that as Fady’s exercise plan increases by a fixed amount each day, it forms an arithmetic sequence. For how long will Fady exercise on the eighteenth day? Answer Example 1: Finding a Specific Term in an Arithmetic Sequence Presented as a Word Problemįady’s exercise plan lasts for 6 minutes on the first day and increases by 4 minutes each day.
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