Arithmetic1

The prime numbers from 1 to 1000 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 By seeing above the table of prime numbers from 1 to 1000 we can observe that 168 prime numbers are there. by seeing the below table we can observe how the prime numbers are distributed. 1-100 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 25 101-200 101, 103, 107

By observing  below  table we will know that 25 prime numbers are existing from 1 to 100. Important points to note are:  Number 1 is not a prime number  Number 2 is a even prime number. SEE ALSO: PRIME NUMBERS SEE ALSO: PRIME NUMBERS-2

LOGIC BEHIND MAGIC SQUARE: In a magic square 3x3, if we take numbers from 1 to 9 then the magic sum equal to 15. The magic square is as follows: 4 9 2  3 5 7 8 1 6 In the above magic square 3x3 magic sum is 15. In the above magic square 3x3 we are used numbers from1 to 9 arranged in 9 boxes. In any direction the sum equal to 15. Row wise  4+9+2=15, 3+5+7=15, 8+1+6=15. Column wise 4+3+8=15, 9+5+1=15, 2+7+6=15. Diagnol wise: 4+5+6=15, 2+5+8=15. The above magic square also can be written as follows: 5-1 5+4 5-3  5-2 5 5+2 5+3 5-4 5+1 In the above figure , shows the relation between middle number and other numbers. In the magic square we are taken numbers from 1 to 9 and number 5 is between 1 to 9. If we write  x in place of 5 in above magic square.                                         X-1

To find the average, first we need to calculate the sum of the elements, then we have to divide the sum of the elements by the no of elements to get the average.                                                Average= sum of elements/ no of elements                 Ex:          The average of first 5 natural numbers                                  sum of 5 natural numbers=1+2+3+4+5=15                                  no of elements = 5                                  average = 15/5 =3                                        

  Odd  numbers are 1,3,5,7,9,…., Odd numbers from 1 to 99=            1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99.      by seeing the above there are 50 odd numbers are there from 1 to 99.

  Odd  numbers are 1,3,5,7,9,…., Odd numbers from 1 to 99=            1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99.      by seeing the above there are 50 odd numbers are there from 1 to 99. 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 Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n 2                                Sum of  odd numbers from 1 to 99: 1+3+5+7+9+. . . . .  50 numbers= 50 2                                                                                                                                                                                                                                                                                         = 50x50          

Even numbers from 2 to 100 Even numbers are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,    54, 56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100. Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6 The above can be written as Sum of first 2 even numbers: 2+4= 6= 2x3=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) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Sum of  even numbers from 2 to 100 = 2+4+6+8+10+. . . . .  50 numbers                                                                           = 50(50+1)                                                                 =50x51                                                                 =2550

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 Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n 2                                Sum of first 100 odd  numbers starting with 1: 1+3+5+7+9+. . . . .  100 numbers                                                                                                           = 100 2                                                                                                                                                                                                                                                                                              =100x100                                                                                                                                                  =   1