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yourmom98
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i am given an formula Sn= n/2[2a+(n-1)d] and i am told to verify the formula represents the sum of n terms of an arithmetic series. How do i verify this?
An arithmetic series is a mathematical sequence of numbers where each term is obtained by adding a constant value to the previous term. For example, in the series 2, 5, 8, 11, the constant value is 3.
The formula for finding the sum of an arithmetic series is: S = (n/2)(a1 + an), where S is the sum, n is the number of terms, a1 is the first term, and an is the last term.
To verify if a series is arithmetic, you can check if the difference between each consecutive term is constant. If the difference is the same for all terms, then the series is arithmetic.
An arithmetic series has a constant difference between each term, while a geometric series has a constant ratio between each term. In other words, in an arithmetic series, the terms increase or decrease by a fixed amount, while in a geometric series, the terms are multiplied or divided by a fixed number.
Yes, an arithmetic series can have an infinite number of terms as long as the difference between each term remains constant. However, the sum of an infinite arithmetic series can only be calculated if the common difference is less than 1.