From cc0fca2840e42e7adfa481fc98c1312fa62cdebf Mon Sep 17 00:00:00 2001
From: Souvik Ghosh <xandersavy@gmail.com>
Date: Wed, 30 Mar 2022 22:27:57 +0530
Subject: [PATCH 1/2] Sum Of Ap by using formula for O(1) time complexity

---
 Arithmetic_Progression/Arithmetic_Progression.c   | 15 ++++++++-------
 Arithmetic_Progression/Arithmetic_Progression.cpp | 15 ++++++++-------
 Arithmetic_Progression/Arithmetic_Progression.go  | 13 +++++++------
 .../Arithmetic_Progression.java                   | 15 ++++++++-------
 4 files changed, 31 insertions(+), 27 deletions(-)

diff --git a/Arithmetic_Progression/Arithmetic_Progression.c b/Arithmetic_Progression/Arithmetic_Progression.c
index 5890de63d6..415513831e 100644
--- a/Arithmetic_Progression/Arithmetic_Progression.c
+++ b/Arithmetic_Progression/Arithmetic_Progression.c
@@ -13,13 +13,14 @@
 // To find sum of the arithmetic progression
 int SumOfAP(int a, int d, int n) 
 { 
-    int sum = 0; 
-    for (int i = 0; i < n; i++) 
-    { 
-        sum = sum + a; 
-        a = a + d; 
-    } 
-    return sum; 
+    // int sum = 0; 
+    // for (int i = 0; i < n; i++) 
+    // { 
+    //     sum = sum + a; 
+    //     a = a + d; 
+    // } 
+    // return sum; 
+    return (n/2)*(2*a+((n-1)*d));
 }
 
 int main() {
diff --git a/Arithmetic_Progression/Arithmetic_Progression.cpp b/Arithmetic_Progression/Arithmetic_Progression.cpp
index 0a6279f978..d77a402e10 100644
--- a/Arithmetic_Progression/Arithmetic_Progression.cpp
+++ b/Arithmetic_Progression/Arithmetic_Progression.cpp
@@ -14,13 +14,14 @@ using namespace std;
 // To find sum of the arithmetic progression
 int SumOfAP (int a, int d, int n) 
 { 
-    int sum = 0; 
-    for (int i = 0; i < n; i++) 
-    { 
-        sum = sum + a; 
-        a = a + d; 
-    } 
-    return sum; 
+    // int sum = 0; 
+    // for (int i = 0; i < n; i++) 
+    // { 
+    //     sum = sum + a; 
+    //     a = a + d; 
+    // } 
+    // return sum; 
+    return (n/2)*(2*a+((n-1)*d));
 }
 
 int main() {
diff --git a/Arithmetic_Progression/Arithmetic_Progression.go b/Arithmetic_Progression/Arithmetic_Progression.go
index b171390174..1e3baea2b0 100644
--- a/Arithmetic_Progression/Arithmetic_Progression.go
+++ b/Arithmetic_Progression/Arithmetic_Progression.go
@@ -14,12 +14,13 @@ import (
 )
 
 func SumOfAP(a int, d int, n int) int {
-    var sum = 0
-    for i := 0; i < n; i++ { 
-        sum = sum + a
-        a = a + d
-    } 
-    return sum    
+    // var sum = 0
+    // for i := 0; i < n; i++ { 
+    //     sum = sum + a
+    //     a = a + d
+    // } 
+    // return sum    
+    return (n/2)*(2*a+((n-1)*d));
 }
 
 func main() {
diff --git a/Arithmetic_Progression/Arithmetic_Progression.java b/Arithmetic_Progression/Arithmetic_Progression.java
index b0a9c18052..2f84af247a 100644
--- a/Arithmetic_Progression/Arithmetic_Progression.java
+++ b/Arithmetic_Progression/Arithmetic_Progression.java
@@ -12,13 +12,14 @@ The nth term of an A.P. is defined as (a + (n - 1)*d)
 
 class Arithmetic_Progression {    
     static int SumOfAP(int a, int d, int n) { 
-        int sum = 0; 
-        for (int i = 0; i < n; i++) 
-        { 
-            sum = sum + a; 
-            a = a + d; 
-        } 
-        return sum; 
+        // int sum = 0; 
+        // for (int i = 0; i < n; i++) 
+        // { 
+        //     sum = sum + a; 
+        //     a = a + d; 
+        // } 
+        // return sum; 
+        return (n/2)*(2*a+((n-1)*d));
     } 
     
     public static void main(String args[]) {

From 631f4c0fc31fcdce817678533fb6d3c31bcbf96f Mon Sep 17 00:00:00 2001
From: Souvik Ghosh <xandersavy@gmail.com>
Date: Wed, 30 Mar 2022 22:31:08 +0530
Subject: [PATCH 2/2] Sum Of AP using formula for O(1) complexity