Created By : Abhinandan Kumar
Reviewed By : Phani Ponnapalli
Last Updated : Mar 27, 2023

Finding the Sum of Sequence isn't difficult anymore with the handy tool Sum of Sequence Calculator. After providing the required inputs you can find out the summation of the sequence in seconds along with the detailed explanation.

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### What is Meant by the Sum of Sequence? Or What is Sigma?

A sequence is a series of numbers where the difference between each successive number is same. It is also called an arithmetic series. So, ‘Sum of Sequence’ is a term used to calculate the sum of all the numbers in the given sequence.

In the given article, find in detail about the Sigma of Sequences and how to find the Sum of sequences. Visit, sequencecalculators.com to meet your daily demands we try to add different calculators regarding several Sequence related concepts.

### How to Find Sum of Arithmetic Sequence?

The step wise explanation of finding the sum of arithmetic sequence is given below:

Step 1:

An arithmetic sequence, an = a1 + (n – 1)d

Here, d is difference between terms of sequence & first term is a1

So, second term is a2 = a1 + d , nth term is an = an-1 + d

Sum, Sn = a1 + a2 + …… + an-1 + [a1 + (n – 1)d]

Step 2:

Need to Reverse the above equation,

Sn = an + (an - d) + (an - 2d)+ …. + [an –(n-1) d]

Step 3:

Add above two equations together & substitute an = a1 + (n – 1)d

Step 4:

Finally, we get the sum of Arithmetic sequence formula to find the summation of sequences at a faster pace.

Sn = n/2 [ 2a1 + (n – 1)d]

### Solved Example on Finding the Sigma of Arithmetic Sequence

Example:

Find the sum of Arithmetic Sequence -5, -2, 1,... up to 10 terms.

Solution:

Given sequence, -5, -2, 1,... up to 10 terms.

Here, a1= -5 and n =10

Sn = n/2[2a1+(n-1)d]

Sn = 10/2[2(-5)+10-13]

Sn = 10/2[-10+27]

Sn = 85

Hence, the sum of the given arithmetic sequence is 85.

### FAQs on Online Summation of Sequence Calculator with Steps

1. What do we call the Sum of a Sequence of numbers?

A series is known as the sum of the terms of a sequence. For Arithmetic or Geometric Sequences, the sum of the first n terms is denoted by Sn.

2. How do you represent the Sum of a Series?

Using summation or sigma notation, a series can be represented in a compact form. , is used to represent the sum.

3. How do you find the number of terms in an Arithmetic Sequence given the sum?

The number of terms in an Arithmetic Sequence can be calculated using the formula, tn = a + (n - 1) d, we can solve for n, where n is the number of terms.