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Arithmetic Mean
An arithmetic mean is what most call it an average in more sophisticated terms. For instance, if somebody says the average of 20 and 30 is 25, it is also the arithmetic mean of the two values of an arithmetic sequence.
The simplest way to calculate the arithmetic mean is simply by taking average i.e. sum up all the values and divide them by the number of values you added together. The arithmetic mean or the average of a number sum indicates the central tendency of the number’s position.
The arithmetic means calculating formula might vary depending on the frequency of each data set variable i.e. the simple or equally-weighted average and the weighted average.
It is commonly used to describe the observations of an experiment or a survey as a parameter in statistical distributions. However, the general formula for computing arithmetic mean could be represented as;
Arithmetic Mean = sum of elements / number of elements
= a1 + a2 + a3 + … + an / n
Also, you can calculate mean value online by using online mean calculator.
Arithmetic Sequence
An arithmetic sequence is a continuous succession of values that always has the same difference between the pair present consecutively. For instance, the difference between 1 and the following number is always 3, for example in sequence 1, 4, 7, 11, 15…….
We constantly add the same number or value to go from one term to another in arithmetic sequence, often known as a linear sequence. However, the value or number we add is called the common difference and the letter d is used to indicate it
Thus an arithmetic sequence is termed whenever the subsequent terms of a series differ by a constant. The constant difference between successive words is referred to as the common difference.
To calculate the arithmetic sequence of a set of numbers having a common difference the formula could be represented as;
an = a1 + (n−1) d
in the equation above, the an represents the nth term, whereas the a1 is the first and d stands for the common difference among the progressive values. Moreover, this formula is also sometimes known as the nth term formula of the arithmetic progression.
Difference Between Arithmetic Mean and Arithmetic Sequence
When read together both the terms, arithmetic sequence and arithmetic mean seem somehow similar. However, after reading the explanation above of each term now you must have got the idea that they are entirely different terms.
The arithmetic mean is the general average of the values or numbers, contrarily the arithmetic sequence is the adding of numbers or values in a sequence by a common difference. Now let’s comparatively see the differences between the two terms.
The arithmetic mean as discussed above clearly is the average, Which is the metric for finding the center of a data et. By adding all values and dividing the sum by the total number of values. The arithmetic means is determined, as the general average formula.
An arithmetic sequence is a sequence of numbers that constitutes a constant value from term to term. Therefore, in an arithmetic sequence, from one value to the next, you always add the same constant value.
Conclusion
Moreover, in an arithmetic sequence is a list of the numbers or values with a constant, i.e. common difference. The arithmetic sequence can start on any value, albeit there must always be the same difference between subsequent terms. This common difference is however not needed or present in arithmetic means.
In the same manner, the calculating formulas for both the values are entirely different. Sum up the number or set of values and then simply divide. The result by the number of the values to compute the arithmetic mean.
In contrast, taking the initial number then summing a value to that number. Then adding the same value to each new term is used to calculate an arithmetic sequence. The common difference is termed this additional value, which is being summed up in all the values in the sequence.
