How can you tell the difference between an and SN?

To find the difference between An and Sn, we subtract Sn from An. Substituting the respective formulas, we get: a + (n-1)d - [n/2 * (2a + (n-1)d)]. Expanding and simplifying this expression yields a more comprehensive understanding of the relationship between An and Sn.

Understanding the problem at hand involves calculating the difference between two important terms in arithmetic progression: An and Sn. An represents the nth term of the sequence, whereas Sn denotes the sum of the first n terms. To find this difference, we must delve into the mathematical expressions that define these terms.

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Let's begin with the nth term, An, in an arithmetic progression. It is given by the formula An = a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number. This formula helps us determine any specific term in the sequence.

Next, we consider Sn, the sum of the first n terms in the arithmetic progression. The formula for Sn is Sn = n/2 * [2a + (n-1)d]. This formula efficiently computes the cumulative sum of the sequence's initial n terms.