Sum of Arithmetic Sequence Formula

The sum of the artithmetic sequence formula is used to calculate the total of all the digits present in an arithmetic progression or series. To recall, arithmetic series of finite arithmetic progress is the addition of the members. The sequence that the arithmetic progression usually follows is (a, a + d, a + 2d, …) where “a” is the first term and “d” is the common difference.

Formula for Sum of Arithmetic Sequence Formula

There are two ways with which we can find the sum of the arithmetic sequence. The formulas for the sum of the arithmetic sequence are given below:

Sum of Arithmetic Sequence Formula
When the Last Term is Given S = n⁄2 (a + L)
When the Last Term is Not Given S = n⁄2 {2a + (n − 1) d}

Notations:

  • “S” is the sum of the arithmetic sequence,
  • “a” as the first term,
  • “d” the common difference between the terms,
  • “n” is the total number of terms in the sequence and
  • “L” is the last term of the sequence.

Also Check: Arithmetic Sequence Formula

Solved Example Using Sum of Arithmetic Sequence Formula

Question: Find the sum of the first 30 terms of the sequence 1, 3, 5, 7, 9 ……

Solution:

Given,

a = 1
d = 2
n = 30

Using the formula: S = n/2 {2a + (n − 1)d}

S = 30/2 {2(1) + (30 − 1)2}

= 900

Also Access
NCERT Solutions for class 10 Maths Chapter 5 Arithmetic Progressions
NCERT Exemplar for class 10 Maths Chapter 5 Arithmetic Progressions
CBSE Notes for Class 10 Maths Chapter 5 Arithmetic Progressions

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  1. how to check whether sum of any terms of sequence is asked