Question # 1: A series is:
1. any list of numbers
2. a summation of quantities whose positions are based upon the natural numbers
3. an arrangement of quantities whose positions are based upon the natural numbers.
Which number is it?
Question # 2: For the rule of 78, for a 12 month period, the last term in the sequence is 12 and the series sums to 78.
For a 14 period, the last term is ? and the series sum is ?.
For a 16 month period, the last term is ? and the series sum is ?.
For a 20 month period, the last term is ? and the series sum is ?.
1) a series is an infinite set based on ordered, summed.
2) http://www.college-cram.com/study/businessmath/presentations/781
It is a series of numbers
Question # 1: Based on the given options, the correct answer for a series would be option 3. A series is an arrangement of quantities whose positions are based upon the natural numbers.
To find the answer, you need to understand the definitions of the terms provided. In this case, a series can be defined as a collection of individual elements or quantities that are arranged in a specific order, where each element is assigned a position based on the natural numbers (1, 2, 3, 4, ...).
Therefore, out of the given options, option 3 best describes what a series is: an arrangement of quantities whose positions are based on the natural numbers.
Question # 2: The rule of 78 is a method used to calculate precomputed interest charges on a loan or debt. In this method, the amount of interest for each period is predetermined and summed up to give a fixed total over the course of the loan.
For a better understanding, let's break down the information provided:
For a 12-month period:
The last term in the sequence is given as 12, meaning the last period in the 12-month series.
The series sums to 78, indicating the total interest charged over the 12-month period.
Now, let's calculate the following scenarios:
For a 14-month period:
To find the last term in the sequence (the term representing the 14th month), you need to subtract 12 (the number of months in the first series) from 14, resulting in 2. Therefore, the last term would be 2.
For the series sum, since the rule of 78 is being used, the sum remains constant at 78 for any duration. So, regardless of the number of months, the series sum for a 14-month period would also be 78.
For a 16-month period:
The last term can be found by subtracting 12 from 16, resulting in 4. Thus, the last term for the 16-month period would be 4.
Similar to the previous case, the series sum remains constant. Therefore, the series sum for a 16-month period would still be 78.
For a 20-month period:
By subtracting 12 from 20, you would get 8. Hence, the last term for the 20-month period would be 8.
Again, the series sum for the 20-month period would still be 78, as the rule of 78 maintains a constant sum regardless of the loan duration.
In summary:
- For a 14-month period, the last term is 2, and the series sum is 78.
- For a 16-month period, the last term is 4, and the series sum is 78.
- For a 20-month period, the last term is 8, and the series sum is 78.