An arithmetic sequence has first term a = 5 and common difference d = 4. how many terms of this sequence must be added to get 4185?

Given that in arithmetic sequence a=5 and common difference, d=4. Thus the number of terms of this sequence that must be added to attain 4185 will be found as follows:
the explicit formula for arithmetic sequence is given by:
sn=n/2(2a+(n-1)d)
where n is the number of terms:
thus plugging in the values we get:
4185=n/2(2*5+(n-1)4)
solving for n we get:
8370=(10+4n-4)
8370=(6+4n)
4n=8364
n=8364/4
n=2091
thus the number of terms will be:
2091