# 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

## 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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