I hope you’ve gone through our previous post which was focused on arithmetic sequence and Basics,

- If not, click here for reading that post.

• So, I’ve revealed the formula of last term of an arithmetic sequence in that post, Now here I’m going to share the formula of finding the ** sum of n terms** of an arithmetic sequence.

Sum of “n” terms of an Arithmetic sequence

• ** Finding Sum of given terms of an AP:-**

let there are n terms in given progression and the sum of those terms are defined as “S” and formulated as,

**S = n/2 [2a + (n-1)d]**

all other values are known i.e.

“a” as first term and

“d” as common difference.

• **This can formula can also be utilised for evaluating other unknown values if sum is given. That means in this there four (S, a, n, d) variables and any one can be calculated if other three are given.**

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- Another form of sequence formula

**S = n/2 [ a+ Tn]****S= [ n (n+1)] / 2**

**S = n/2 [ 2a + (n-1)d]**

**for n consecutive number**

**a= 1, d= 1**

**so,**

**S = n/2 [ 2×1 + (n-1)×1]**

**= n/2 [ 2 + n-1]**

**= n/2 [ n+1 ]**

**hence,**

**S = [n( n+ 1 )] / 2**