Arithmetic sequence
a sequence in which each term is found by adding the same number to the previous term
An arithmetic sequence is a sequence of numbers in which each term is determined by adding or subtracting a fixed value (called the common difference) to the preceding term. For example, the sequence 2, 5, 8, 11, 14, … is an arithmetic sequence with a common difference of 3.
The nth term of an arithmetic sequence can be described using the formula:
an = a1 + (n – 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
The sum of the first n terms of an arithmetic sequence can be calculated using the formula:
Sn = (n/2)(2a1 + (n-1)d)
where Sn is the sum of the first n terms, a1 is the first term, n is the number of terms, and d is the common difference.
Arithmetic sequences have many practical applications in everyday life, such as calculating loan payments, determining the speed of a moving object at a given time, and predicting future earnings based on current trends.
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