20: MULTIPLY 3 CONSECUTIVE NUMBERS

SUTRA (Algorithm):

Prod. of 3 Consec. Numbers = Midlde3 - Middle

[ OR ]

Prod. of 3 Consec. Numbers = Midlde x (Middle2 - 1)

Demonstration (1): 3 x 4 x 5 = ?

3 x 4 x 5 = 43 - 4 = 64 - 4 = 60
or
3 x 4 x 5 = 4 (42 - 1) = 4 (15) = 60

Demonstration (2): 11 x 12 x 13 = ?

11 x 12 x 13 = 123 - 12 = 1728 - 12 = 1716
or
11 x 12 x 13 = 12 (144 - 1) = 12 x 143 = 1716

Demonstration (3): 19 x 20 x 21 = ?

19 x 20 x 21 = 203 - 20 = 8000 - 20 = 7980
or
19 x 20 x 21 = 20 (400 - 1) = 20 x 399 = 7980

Verify by Actual Working:

  1. 14 x 15 x 16 = 153 - 15 = 3375 - 15 = 3360

  2. 14 x 15 x 16 = 15 (152 - 1) = 15 x 224 = 3360
  3. 21 x 22 x 23 = 22 (484 - 1) = 2 x 11 x 483
    = 2 x 5313 = 10626
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