Arithmetic Sequence

In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time ... infinitely.

In General we could write an arithmetic sequence like this: {a, a+d, a+2d, a+3d, ... }

where:

• a is the first term, and
• d is the difference between the terms (called the "common difference")

Rule

We can write an Arithmetic Sequence as a rule: x_n = a + d(n-1)

Summing an Arithmetic Series 

To sum up the terms of this arithmetic sequence:

a + (a+d) + (a+2d) + (a+3d) + ...

use this formula: 

Question

Given a 100 terms of arithmetic sequence, first term is  3, and the difference is 4, a new term is inserted between each tow terms and a new arithmetic sequence is received. What is the sum of terms of the new sequence?