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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.
The step wise explanation of finding the sum of arithmetic sequence is given below:
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]
Need to Reverse the above equation,
Sn = an + (an - d) + (an - 2d)+ …. + [an –(n-1) d]
Add above two equations together & substitute an = a1 + (n – 1)d
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]
Find the sum of Arithmetic Sequence -5, -2, 1,... up to 10 terms.
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.
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.