Suppose you had an arithmetic sequence such as 1, 4, 7, 10, 13, ..... and you wish to find the sum of the first 50 terms of the sequence. You could take all 50 terms and add them together, but that is time consuming. There are some simple formulas you can use to get the answer.
Sn (sum of the first n terms) is the average of the first and last term multiplied by the number of terms. Written as a formula this is Sn = n[(a1 + an)/2] where a1 is the first term and an is the last term.
To find the 50th term we use the formula
an = a1 + (n-1)d, where d is the common difference between the terms. You can clearly see that common difference is 3.
so the 50th term is 1 + (50-1)(3) = 148
Now to get the sum, we get Sn = 50(1 + 148)/2 = 25(149) = 3,725