Question

what is the difference between An and Sn in arithmetic progression?

Answer 1

$S_n$ is the sum of a n th terms of a a series in AP
$A_n$ is the n th term of an AP

$S_n=\frac{n}{2}[2a+(n-1)d]$

$A_n=a+(n-1)d$

Where n = number of terms 
a = first term 
d= common difference

in a AP

Answer 2

Given; Sn and An

To Find; the difference between An and Sn in arithmetic progression

Solution; We have to find the difference between An and Sn

The nth term of an AP, an = a+(n-1)d

Sum of n terms = n/2[2a + (n - 1)d]

difference = a+nd-d +na +n²d/2 -nd/2

The nth term of an AP, an = a+(n-1)dSum of n terms = n/2[2a + (n - 1)d]difference = a+nd-d +na +n²d/2 -nd/2

Hence the difference is a+nd-d +na +n²d/2 -nd/2