Find s25 for 3 + 7 + 11 + 15

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

S25 = 25 * (a1+a25) / 2

S25 = 25 * (3+99) / 2

S25 = 25 * (102) / 2

S25 = 2550/2

S25 = 1275

The final answer is 1275