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

Practise This Question

In the given figure, AD = BC. What is the length of AB if DC = 4 cm?

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