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(n1)
Summing an Arithmetic Series
To sum up the terms of this arithmetic sequence:
a + (a+d) + (a+2d) + (a+3d) + ...
use this formula:
see http://blossoms.mit.edu/videos/files/arabic_english_subtitles/amazing_problems_arithmetic_and_geometric_sequences_arabic_eng information
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?
