Posted by **Anonymous** on Friday, March 30, 2012 at 12:23pm.

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**, Friday, March 30, 2012 at 2:35pm
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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