# Math

posted by Anonymous

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)
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

1. 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

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