The common difference is d = 4 because we add 4 to each term to get the next one.
The starting term is a1 = 3
The nth term of this arithmetic sequence is an = a1 + d(n-1) an = 3 + 4(n-1) an = 3 + 4n-4 an = 4n - 1
Plug in n = 25 to find the 25th term an = 4n - 1 a25 = 4*25 - 1 a25 = 100 - 1 a25 = 99
So we're summing the series : 3+7+11+15+...+99
We could write out all the terms and add them all up. That's a lot more work than needed though. Luckily we have a handy formula to make things a lot better The sum of the first n terms is Sn. The formula for Sn is Sn = n*(a1+an)/2
Plug in n = 25 to get Sn = n*(a1+an)/2 S25 = 25*(a1+a25)/2
Then plug in a1 = 3 and a25 = 99. Then compute to simplify
