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    E:\Working\Orange_Education\TouchPad_Maths_4\Open_Files\Chap_08\Chap_08
                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                Number Patterns

                Numbers can also be arranged according to a pattern. Observe the following number
                pattern.

                                             2, 4, 6, 8, 10, 12, 14, ...

                In this pattern, there is a relation between consecutive numbers in which 2 is added
                each time to give the next number.

                Patterns in Addition

                    1.  Addition of two consecutive numbers                                 1      +     2     =     3

                        Observe the  pattern  in the  addition  of two    2                        +     3     =     5
                        consecutive numbers.                                                3      +     4     =     7
                                                                                           ____  +  ____  =  ____
                        We see that the sums are consecutive odd numbers
                        starting from 3.

                  2.  Addition of three consecutive numbers

                           1     +     2     +    3     =     6         Here, we observe  that the sums  are
                           2     +    3      +     4    =     9         multiples of 3. Also, the sum is thrice the

                          3      +     4     +    5     =     12        middle term.
                         ____  +  ____  +  ____  =  ____

                  3.  Addition of four consecutive numbers

                                                                                   Here, we observe that the sum
                           1     +     2     +     3     +     4    =    10        increases  by  4  at  each  step.
                           2     +     3     +     4     +    5     =    14        Also, the  sum  in each  case

                           3     +     4     +     5     +    6     =    18        is twice  the sum of the two
                                                                                   middle terms.
                         ____  +  ____  +  ____  +  ____  =  ____

                  4.  Addition of five consecutive numbers

                                                                                             Here, we observe that
                           1     +     2     +    3     +     4     +    5     =    15       the sums are multiples

                           2     +    3      +     4    +     5     +    6     =    20       of 5. Also, the sum is
                          3      +     4     +    5     +     6     +     7    =    25       five times  the middle
                                                                                             term.
                         ____  +  ____  +  ____  +  ____  +  ____  =  ____

                       140       Mathematics 4

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