Reasonable Conjectures
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Reasonable Conjectures

2 7 4 9 6 11 8 13

20 A 18 B 16 C

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Reasonable Conjectures

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Sep 18, 2011
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Reasonable Conjectures
by: Staff


The question:


2 7 4 9 6 11 8 13

20 A 18 B 16 C



The answer:


2 7 4 9 6 11 8 13

Reasonable conjecture for the next 6 numbers

10 15

12 17

14 19

The next 6 numbers are:

10 15 12 17 14 19


Reasoning:

The FIRST NUMBER in the sequence is 2

EVERY OTHER NUMBER in the sequence is a CONSECUTIVE EVEN NUMBER. Instead of 2 3 4 5 6 7 8, the odd numbers are left out, leaving the sequence (2, 4, 6, 8, . . .).

In between the sequence of consecutive even numbers is A SEQUENCE OF CONSECUTIVE ODD NUMBERS. The sequence of odd numbers begins with 7. This sequence of odd numbers is (7, 9, 11, 13 . . .).

The final sequence is a combination of the even and odd sequences:

2 7

4 9

6 11

8 13

10 15

12 17

14 19

The final sequence, including the original numbers and the Reasonable Conjecture for the next 6 numbers is:

2 7 4 9 6 11 8 13 10 15 12 17 14 19

--------------------------------------------------------------------------------

20 A 18 B 16 C

Reasonable conjecture for the next 6 elements in the sequence

14 D

12 E

10 F

The next 6 elements are:

14 D 12 E 10 F



Reasoning:

The FIRST element in the sequence is 20

EVERY OTHER NUMBER in the sequence is an EVEN NUMBER which is equal to the last even number minus 2: (20, 18, 16, . . .).

In between the numbers of this (reverse) even number sequence is another sequence: the LETTERS OF THE ALPHABET arranged in ALPHABETICAL ORDER {A, B, C . . .}.

20 A

18 B

16 C

14 D

12 E

10 F


The final sequence, including the original elements and the Reasonable Conjecture for the next 6 elements in the sequence is:

20 A 18 B 16 C 14 D 12 E 10 F




Thanks for writing.

Staff
www.solving-math-problems.com



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