Arithmetic1

The example for consecutive even numbers is 2,4,6,8,10,. . . . The above consecutive even number series can be  written as         2,2+2,2+4,2+6,2+8,2+10, . . . . . In the above series if we replace 2 in every number by “x”. Then the above series can be rewritten as         X, X+2,X+4,X+6, X+8, X+10, X+12,. . . . . . . From the above series we can written as 2 consecutive even numbers = X, X+2 3 consecutive even numbers  =        X, X+2,X+4 4 consecutive even numbers =  X, X+2,X+4,X+6 5 consecutive even numbers =   X, X+2,X+4,X+6, X+8 Now we see the following problem the sum of three consecutive even numbers is 234. what are those numbers We can write three consecutive even number series as  3 consecutive even numbers =   X, X+2,X+4.    Sum of consecutive even numbers = X+ X+2+X+4                                                               234=X+X+X+2+4                                                               234= X+X+X+2+4                  

The example for consecutive even numbers is 2,4,6,8,10,. . . . The above consecutive even number series can be written as         2,2+2,2+4,2+6,2+8,2+10, . . . . . In the above series if we replace 2 in every number by “x”. Then the above series can be rewritten as         X, X+2,X+4,X+6, X+8, X+10, X+12,. . . . . . . From the above series we can written as 2 consecutive even numbers = X, X+2 3 consecutive even numbers  =        X, X+2,X+4 4 consecutive even numbers =  X, X+2,X+4,X+6 5 consecutive even numbers =   X, X+2,X+4,X+6, X+8 Now we see the following problem the sum of three consecutive even numbers  is 138. what is the smallest/ biggest of these numbers We can write three consecutive even number series as  3 consecutive even numbers =   X, X+2,X+4.    Sum of consecutive even numbers = X+ X+2+X+4                                                               138 =X+X+X+2+4                                                               138= X+X+

The example for consecutive even numbers  is 2,4,6,8,10,. . . . The above consecutive even number series can be written as         2,2+2,2+4,2+6,2+8,2+10, . . . . . In the above series if we replace 2 in every number  by “x”. Then the above series can be rewritten as         X, X+2,X+4,X+6, X+8, X+10, X+12,. . . . . . . From the above series we can written as 2 consecutive even numbers = X, X+2 3 consecutive even numbers  =   X, X+2,X+4 4 consecutive even numbers =  X, X+2,X+4,X+6 5 consecutive even numbers =   X, X+2,X+4,X+6, X+8 Now we see the following problem the sum of three consecutive even numbers is 42. what is the smallest of these numbers We can write three consecutive even number series as  3 consecutive even numbers =   X, X+2,X+4.    Sum of consecutive even numbers = X+ X+2+X+4                                                               42=X+X+X+2+4                                                               42= X+X+X+2+4          

The example for consecutive  even numbers is 2,4,6,8,10,. . . . The above consecutive even number series can be written as         2,2+2,2+4,2+6,2+8,2+10, . . . . . In the above series if we replace 2 in every number by “x”. Then the above series can be rewritten as         X, X+2,X+4,X+6, X+8, X+10, X+12,. . . . . . . From the above series we can written as 2 consecutive even numbers = X, X+2 3 consecutive even numbers  =        X, X+2,X+4 4 consecutive even numbers =  X, X+2,X+4,X+6 5 consecutive even numbers =   X, X+2,X+4,X+6, X+8 Now we see the following problem the average of three consecutive even numbers is 72 what are the smallest of these numbers. We can write three consecutive even number series as  3 consecutive even numbers =   X, X+2,X+4.   Average = sum of elements/ no of elments Average = (X+ X+2+X+4)/3            72=(X+X+X+2+4)/3            72X3= X+X+X+2+4           216= 3X+2+4           216=3X+6           216-6=3X        

Even numbers  are 2,4,6,8,10,…. Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) if you see  above there is particular pattern is observed while adding first even numbers. the sum of the first 5 even numbers is 5(5+1) the sum of the first 10 even numbers is 10(10+1) T he formula for Sum of first n even  numbers:1+3+5+7+9+. . n numbers= n(n+1)      Since the formula for Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1)

Odd  numbers are 1,3,5,7,9,…. Now we will see the sum of  elements: Sum of first 2 odd  numbers: 1+3= 4= 2 2 Sum of first 3 odd  numbers: 1+3+5= 9= 3 2 Sum of first 4 odd  numbers: 1+3+5+7=16= 4 2 Sum of first 5 odd  numbers: 1+3+5+7+9 = 25 = 5 2 if you see  above there is particular pattern is observed while adding first odd numbers. the sum of the first 5 numbers is  5 2 the sum of the first 10 numbers is 10 2 T he formula for Sum of first n odd  numbers: 1+3+5+7+9+. . .  n numbers= n 2