# Sum Of Arithmetic Sequence Formula

## Sum Of Arithmetic Sequence Formula

Prior to learning the Sum Of Arithmetic Sequence Formulas, students must be able to define an arithmetic sequence. Arithmetic sequences are collections of numbers where each term is the sum of the terms before it and a fixed number. A common difference is a name given to this predetermined amount. The differences between every two successive terms in an arithmetic sequence are the same.

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What Is the Sum of Arithmetic Sequence Formula?

The formula to add up all the terms in an arithmetic sequence is known as the sum of the arithmetic sequence formula. Students are aware that after adding the members, an arithmetic series with finite arithmetic progress is produced, which is represented by (a, a + d, a + 2d,…), where “a” stands for the first term and “d” for the common difference.

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### Sum of Arithmetic Sequence Formula

Take into account a mathematical sequence (AP) where the first term is a and the common difference is d.

Formula 1: The sum of the first n terms of an arithmetic sequence where

the nth term is not known is given by:

Sn = n/2[2a+(n−1)d]

Where

Sn = the sum of the arithmetic sequence,

a = the first term,

d = the common difference between the terms,

n = the total number of terms in the sequence and

an = the last term of the sequence.

Formula2: The following gives the sum of the first n terms of an arithmetic series when the nth term, Sn, is known is given by:

Sn=n/2[a1+an]

Where

Sn = the sum of the arithmetic sequence,

a1 = the first term,

d = the common difference between the terms,

n = the total number of terms in the sequence and

an = the last term of the sequence.

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### Derivation of Sum of Arithmetic Series Formula

Every term after the first in an arithmetic sequence is obtained by adding a constant known as the common difference.

Students must comprehend the process used to arrive at the Sum Of Arithmetic Sequence Formulas. They must be familiar with the derivation because exams frequently contain such simple questions. They should therefore be familiar with the background of the Sum Of Arithmetic Sequence Formula. The Sum Of Arithmetic Sequence Formula is something that requires practice to fully comprehend. Students are expected to use the Sum Of Arithmetic Sequence Formula to respond to common queries.

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### Examples Using Sum of Arithmetic Sequence Formula

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