# What is the formula for the sum of an arithmetic sequence?

##### 2 Answers

# S_n = n/2(2a+(n-1)d) #

#### Explanation:

Suppose we have an AP with first term

# S_n = a + (a+d) + (a+2d) + ... + (a+(n-1)d) #

Writing the same sum, but in reverse, we get:

# S_n = (a+(n-1)d) + ... (a+2d) + (a+d) + a #

If we add both of these we get:

# 2S_n = (2a+(n-1)d) + (2a+(n-1)d) + ... + (2a+(n-1)d) #

# \ \ \ \ \ = n(2a+(n-1)d) #

Leading to the standard AP summation formula

# S_n = n/2(2a+(n-1)d) #

The sum of an arithmetic sequence is given by

#### Explanation:

Let

Adding up the two equations term by term we get

*Notice how the

Since we have