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The objective of this number trick is to find the sum of a given set of 10 numbers before students using calculators can complete the process. Students select the first two numbers, all others are generated by adding the preceding two numbers.Let's just do a few examples to get the idea.
Students select the first two numbers and they are entered in numerical order
- trial 1 trial 2 trial 3 general 1 3 6 4 a 2 7 8 6 b 3 10 14 10 a + b 4 17 22 16 a + 2b 5 27 36 26 2a + 3b 6 44 58 42 3a + 5b 7 71 94 68 5a + 8b 8 115 152 110 8a + 13b 9 186 246 178 13a + 21b 10 301 398 288 21a + 34b - --------------- --------------- --------------- --------------- sum: 781 1034 748 55a + 88b = - 11 x 71 = 781 11 x 94 = 1034 11 x 68 = 748 11(5a + 8b) The "trick" to solving this problem quickly is to multiply the 7th term by 11 to find the sum of the 10 numbers.
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