How to Solve Arithmetic Series

How to Solve Arithmetic Series

An arithmetic series is a sequence of numbers in which each term is the sum of the previous term and a constant common difference. The general formula for an arithmetic series is:

\(a + (a + d) + (a + 2d) + … + (a + (n-1)d)\) \(=\) \(\frac{n(a + (a + (n-1)d))}{2}\)

Where:

  • \(a\) is the first term of the series
  • \(d\) is the common difference
  • \(n\) is the number of terms in the series

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Step-by-step to Solve Arithmetic Series

To solve an arithmetic series, you can use the following steps:

  1. Identify the first term \((a)\), the common difference \((d)\), and the number of terms \((n)\) in the series.
  2. Use the general formula of an arithmetic series to find the sum of the series: \(\frac{n(a + (a + (n-1)d))}{2}\)
  3. If you want to find a specific term of the series, you can use the formula: \(a + (n-1)d\)

For example, if you have an arithmetic series with \(a = 2\), \(d = 3\) and \(n = 4\), the sum of the series is: \(\frac{n(a + (a + (n-1)d)}{2}\) \(=\) \(\frac{4(2 + (2 + (4-1)3))}{2}\) \(=\) \(\frac{4(2 + 2 + 9)}{2}\) \(=\) \(\frac{4(13)}{2} = 52\)

If you want to find the 4th term of the series , you can use the formula: \(a + (n-1)d = 2 + (4-1)3 = 2 + 3 = 5\)

Arithmetic series are widely used in various fields such as finance, science, statistics, and many more.

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