Arithmetic1

Product of two consecutive odd numbers : Even numbers are 1,3,5,7,9,11,13,15,17,19,21,23,25,..... Odd  number means when we divide a number with 2,then the remainder is equal to one. Difference between the two odd numbers is 1. Now we will discuss the product of two odd  numbers. Now the product of two even numbers assumed to be 5x7 can be written as (6-1)x(6+1).                              5x7= (6-1)x(6+1) From the above we write general formula as 5x7= (6-1)x(6+1)=6 2 -1 2  =36-1=35 Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent odd numbers. Column 3 represent the product of two adjacent odd numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two odd  numbers. NUMBER1  NUMBER2 PRODUCT NEAREST SQUARE NO. 1 3 3 4 3 5 15 16 5 7 35

Product of two consecutive even numbers : Even numbers are 2,4,6,8,10,12,14,16,18,20,22........ Even number means when we divide a number with 2,then the remainder is equal to zero. Difference between the two even numbers is 1. Now we will discuss the product of two even numbers. Now the product of two even numbers assumed to be 4x6 can be written as (5-1)x(5+1).                              4x6= (5-1)x(5+1) From the above we write general formula as 4x6= (5-1)x(5+1)=5 2 -1 2  =25-1=24 Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent even numbers. Column 3 represent the product of two adjacent even numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two even numbers. NUMBER1 NUMBER2 PRODUCT NEAREST SQUARE NO. 2 4 8 9 4 6 24 25 6 8 48

n  1 n  2 n  3 n  4 n  5 1  0 =1 2  0 =1 3  0 =1 4  0 =1 5  0 =1 1  1 =1 2  1 =2 3  1 =3 4  1 =4 5  1 =5 1  2 =1 2  2 =4 3  2 =9 4  2 =16 5  2 =25 1  3 =1 2  3 =8 3  3 =27 4  3 =64 5  3 =125 1  4 =1 2  4 =16 3  4 =81 4  4 =256 5  4 =625 1  5 =1 2  5 =32 3  5 =243 4  5 =1024 5  5 =3125 1  6 =1 2  6 =64 3  6 =729 4  6 =4096 5  6 =15625 1  7 =1 2  7 =128 3  7 =2187 4  7 =16384 5  7 =78125 1  8 =1 2  8 =256 3  8 =6561 4  8 =65536 5  8 =390625 1  9 =1 2  9 =512 3  9 =19683 4  9 =262144 5  9 =1953125 1  10 =1 2  10 =1024 3  10 =59049 4  10 =1048576 5  10 =9765625 n  6 n  7 n  8 n  9 n  10 6  0 =1 7  0 =1 8  0 =1 9  0 =1 10  0 =1 6  1 =6 7  1 =7 8  1 =8 9  1 =9 10  1 =10 6  2 =36 7  2 =49 8  2 =64 9  2 =81 10  2 =100 6  3 =216 7  3 =343 8  3 =512 9  3 =729 10  3 =1000 6  4 =1296 7  4 =2401 8  4 =4096 9  4 =6561 10  4 =10000 6  5 =7776 7  5 =16807 8  5 =32768 9  5 =59049 10  5 =100000 6  6 =46656 7  6 =117649 8  6 =262144 9  6 =531441 10  6 =1000000 6  7 =279936 7  7 =

If you observe the sum of each digit in the Multiplication of two consectuive no.  pattern repeating:  2 6 3  2 3 6 2 9 9  n X n+1 Multiplication of two consectuive no. Sum of two digits 1X2 2 2 2X3 6 6 3X4 12 3 4X5 20 2 5X6 30 3 6X7 42 6 7X8 56 2 8X9 72 9 9X10 90 9 10X11 110 2 11X12 132 6 12X13 156 3 13X14 182 2 14X15 210 3 15X16 240 6 16X17 272 2 17X18 306 9 18X19 342 9 19X20 380 2 20X21 420 6 21X22 462 3 22X23 506 2 23X24 552 3 24X25 600 6 25X26 650 2 26X27 702 9 27X28 756 9