[Explanation] Arithmetic Progression (#107)

* [Explaination] AP & GP

* AP repaired & GP removed

* Renamed for AP

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Author: aminoxix

en/Basic Math/Arithmetic Progressions.md

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+# Arithmetic Progression
+
+A sequence of numbers is said to be in an `Arithmetic progression` if the difference between any two consecutive terms is always the same. In simple terms, it means that the next number in the series is calculated by adding a fixed number to the previous number in the series.
+For example, 2, 4, 6, 8, 10 is an AP because the difference between any two consecutive terms in the series (common difference) is same (4 - 2 = 6 - 4 = 8 - 6 = 10 - 8 = 2).
+<p align="center">
+    <img width="60%" src="https://user-images.githubusercontent.com/75872316/122635132-ce38d100-d0ff-11eb-8fdf-2e14a9f640cc.png">
+</p>
+
+**Facts about Arithmetic Progression:**
+
+1. Initial term: In an arithmetic progression, the first number in the series is called the initial term.
+2. Common difference: The value by which consecutive terms increase or decrease is called the `common difference`.
+3. The behavior of the arithmetic progression depends on the common difference `d`. If the common difference is positive, then the members (terms) will grow towards positive infinity. But if the common difference is negative, then the members (terms) will grow towards negative infinity.
+
+**Formula of the nth term of an A.P:**
+
+`a` is the initial term, and `d` is a common difference. Thus, the explicit formula is:
+<p align="center">
+    <img width="60%" src="https://user-images.githubusercontent.com/75872316/122635193-25d73c80-d100-11eb-9015-344d36633704.png">
+</p>
+
+**Formula of the sum of first nth term of A.P:**
+
+<p align="center">
+    <img width="60%" src="https://user-images.githubusercontent.com/75872316/122635260-7a7ab780-d100-11eb-82a5-8ceeba3aff03.png">
+</p>
+
+**General Formulas to solve problems related to Arithmetic Progressions:**
+
+ If `a` is the first term and `d` too, that would be a common difference:
+- **nth term of an AP** = `a + (n-1)*d`.
+- **Arithmetic Mean** = `Sum of all terms in the AP / Number of terms in the AP`.
+- **Sum of ‘n’ terms** of an AP = 0.5 n (first term + last term) = `0.5 n [ 2a + (n-1) d ]`.
+
+# Source
+
+- [Arithmetic Progression](https://www.geeksforgeeks.org/arithmetic-progression)
+
+# YouTube
+
+- [Video URL for concept](https://youtu.be/gua96ju_FBk)
+- [Video for understanding AP Dynamic Programming in C++](https://youtu.be/U_qtSRQYoPs)