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March 26, 2017

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Name School Team
Event 3: Logic and Reasoning (with calculators) 5th/6th grade Math Meet ‘08
For each number pattern, fill in the next five terms. (2 pts. each blank)
ANSWER KEY
1st
term
2nd
term
3rd
term
4th
term
5th
term
6th
term
7th
term
8th
term
9th
term
10th
term
1)
2)
3)
4)
1 2 5 10 17 26 37 50 65 82
1 2 6 15 31 56 92 141 205 286
1 3 9 19 33 51 73 99 129 163
1 4 11 24 43 72 109 152 205 266

  • Math - ,

    1 2 5 10 17 26 37 50 65 82

    If you subtract 1 from every number is should be obvious.

    0 1 4 9 16 25 36 64 81

    These are the perfect squares. So the answer is:

    n ^ 2 + 1

    Next nunbers :

    10 ^ 2 + 1 = 100 + 1 =101

    11 ^ 2 + 1 = 121 + 1 = 122

    13 ^ 2 + 1 = 169 + 1 = 170

    14 ^ 2 + 1 = 196 + 1 = 197

    15 ^ 2 + 1 = 225 + 1 = 226



    1 4 9 16 31 56 92 141 205 286

    In the second pattern, the differences are 1,4,9,16,25,36,49,64,81 which are square numbers.

    Next nunbers :

    286 + 10 ^ 2 = 286 + 100 = 386

    386 + 11 ^ 2 = 386 + 121 = 507

    507 + 12 ^ 2 = 507 + 144 = 651

    651 + 13 ^ 2 = 651 + 169 = 820

    820 + 14 ^ 2 = 820 + 196 = 1016



    1 3 9 19 33 51 73 99 129 163


    2 n ^ 2 + 1


    Next numbers:

    2 * 10 ^ 2 + 1 = 2 * 100 + 1 = 200 + 1 = 201

    2 * 11 ^ 2 + 1 = 2 * 121 + 1 = 242 + 1 = 243

    2 * 12 ^ 2 + 1 = 2 * 144 + 1 = 288 + 1 = 289

    2 * 13 ^ 2 + 1 = 2 * 169 + 1 = 338 + 1 = 339

    2 * 14 ^ 2 + 1 = 2 * 196 + 1 = 392 + 1 = 393




    1 4 11 24 43 72 109 152 205 266

    The differences are 3,7,13,19,29,37,43,53,61

    which are every other prime number

    Nex numbers :

    266 + 67 = 333

    333 + 73 = 406

    406 + 83 = 489

    489 + 97 = 586

    586 + 103 = 689

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