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Reasonable Conjectures
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Reasonable Conjectures












































Two separate series of numbers and letters are shown below.

Determine the sequential pattern of each, and predict the next several number and letters in the series. This may be the combination of two or more series.

2 7 4 9 6 11 8 13

20 A 18 B 16 C

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Sep 18, 2011
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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