Question

Make a conjecture about the rules these patterns follow.

1. 3, 6, 9, 12, 15

2. 9, 3, 1, 1/3, 1/9

3. a, c, e, g, i, k, m

4. 0, 5, -2, 3, -4, 1, -6

5. 4, 8, 16, 32, 64, 128

6, 0.1, 0.01, 0.001, 0.0001

Answer 1

Make a conjecture about the rules these patterns follow.

1. 3, 6, 9, 12, 15

2. 9, 3, 1, 1/3, 1/9

3. a, c, e, g, i, k, m

4. 0, 5, -2, 3, -4, 1, -6

5. 4, 8, 16, 32, 64, 128

6, 0.1, 0.01, 0.001, 0.0001

Answer 2

Explanation:

1) 3, 6, 9, 12, 15

• 6 - 3 = 9 - 6 = 12 - 9 = 15 - 2
• Each term is 3 more than the previous term.

2) 9, 3, 1, 1/3, 1/9

• 3/9 = 1/3 = (1/3)/1 = (1/9)/(1/3) = 1/3
• Each term is 3 times less then the previous term.

3) a, c, e, g, i, k, m

• a = 1, c = 3, e = 5, g = 7, i = 9, k = 11, m = 13
• Each letter is 2 places right from the previous letter of English alphabet

4) 0, 5, -2, 3, -4, 1, -6

• 5 - 0 = 5, -2 - 5 = -7
• 3 - (-2) = 5, -4 - 3 = -7
• 1 - (-4) = 5, -6 - 1 = - 7
• Each odd numbered term is 7 less than the previous term, each even numbered term is 5 more than the previous term

5) 4, 8, 16, 32, 64, 128

• 8/4 = 16/8 = 32/16 = 64/32 = 128/64 = 2
• Each term is twice the previous term

6) 0.1, 0.01, 0.001, 0.0001

• 0.1/0.01 = 0.01/0.1 = 0.001/0.01 = 0.0001/0.001 = 0.1
• Each term is 10 times less than the previous term