How to Calculate the Sum of an Arithmetic Series | Formula and Step-by-Step Guide

formula for sum of arithmetic series

The formula for finding the sum of an arithmetic series consists of two components: the number of terms in the series (denoted by “n”), and the average of the first and last term (denoted by “S”)

The formula for finding the sum of an arithmetic series consists of two components: the number of terms in the series (denoted by “n”), and the average of the first and last term (denoted by “S”). The sum of an arithmetic series can be calculated using the following formula:

S = (n/2)(a + l)

Where:
S = sum of the arithmetic series
n = number of terms in the series
a = first term of the series
l = last term of the series

To better understand this formula, let’s break it down into smaller parts:

1. Finding the average of the first and last term:
The average of the first and last term of an arithmetic series is given by (a + l)/2. It represents the middle value of the series.

2. Determining the number of terms in the series:
The number of terms in the series, denoted by ‘n,’ represents the count of terms included in the sequence.

3. Calculating the sum:
To calculate the sum of the arithmetic series, multiply the number of terms by the average of the first and last term. Multiply (n/2) by (a + l) to obtain the sum, denoted by ‘S’.

It’s important to note that “a” and “l” represent the first and last terms respectively, while “n” represents the number of terms in the arithmetic series. Make sure to use the correct values in the formula to obtain an accurate result.

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