First consider smaller example...
say list given = {3,1,2} and say you want to search element '2' in sequential way.So first you will visit first element and compare it with '2' .If it is '2' then your search will end at first element with only 1 comparison. But if it is not equal to '2',then you compare it with second element. so second element is '1' so again search was unsuccessful and comparison required was total '2' i.e. b/w '2' & '3' and b/w '2' & '1' and so on.
So if required element is found at first position , no of comparison = 1;
if required element is found at second position , no of comparison = 2 ...and so on.
Now since our list is not sorted so it can be anything e.g. list can be {1,2,3} or {3,2,1} or {2,3,1}etc.So the element we are looking for may be present at any of these three positions with equal chances of 1/3.
Now consider our list containing 'n' elements. So element to be searched can be present at any of these 'n' positions in the list with equal chance(probability) of 1/n.
Total comparison required = No.of comparison if element present in 1st position + No.of comparison if element present in 2nd position + .......+ No.of comparison if element present in nth position
= 1 + 2 + 3+ ......+n = n(n+1)/2
Since there are 'n' elements in the list.
So avg. no. of comparison = Total comparison/total no of elements = [n(n+1)/2] / n = (n+1)/2.