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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 
Bosnian,
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