1+3+5+7+9+...+99 -100-99-98-...-2-1-0+1+2+48+49+50

Bab Pola Bilangan
Matematika SMP Kelas VII

1] 1 + 3 + 5 + .... + 99
1 + 99 = 100
3 + 97 = 100
5 + 95 = 100
7 + 93 = 100
9 + 91 = 100
              ------- +
               500

11 + 89 = 100 → 100 x 5 = 500
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21 + 79 = 100 → 100 x 5 = 500
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31 + 69 = 100 → 100 x 5 = 500
----------------------------------------------
41 + 59 = 100 → 100 x 5 = 500

hasil = 500 + 500 + 500 + 500 + 500 = 2.500



2]  -100 - 99 - ..... + 0 + 1 + 2 + 3 + .... + 50

-50 + 50 = 0
-49 + 49 = 0
.
.
-1 + 1 = 0

tersisa -100 - 99 - 98 - ... - 52 - 51 = ?

-100
-51 - 99 = -150
-52 - 98 = -150
-53 - 97 = - 150
-54 - 96 = -150
-55 - 95 = - 150
- 56 - 94 = - 150
- 57 - 93 = - 150
- 58 - 92 = - 150
- 59 - 91 = -150
-50 - 90 = -150
                -------- +
                   -150 x 10 = -1.500

-61 sampai -70 = -1.500

-71 - 79 = -150
-72 - 78 = -150
- 73 - 77 = - 150
- 74 - 76 = - 150
                ------------ +
                  -600

total = -100 - 1.500 - 1.500 - 600 - 75 = -3.775