Basic Mathematics for College Students

A-24 Appendix III Inductive and Deductive Reasoning

Solution

Since each successive number is 2 less than the previous one, the next number in

the sequence is  8 2, or 10.

This number is This number is This number is

2 less than the 2 less than the 2 less than the

previous number. previous number. previous number.

2, 4,6, 8 , ....

Self Check 2

Find the next number in the

sequence 0.1,0.3,0.5,

0.7,....

Now TryProblem 15

EXAMPLE (^3) Find the next letter in the sequence A, D, B, E, C, F, D,....
StrategyWe will create a letter–number correspondence and rewrite the
sequence in an equivalent numerical form.
WHYMany times, it is easier to determine the pattern if we examine a sequence
of numbers instead of letters.
Solution
The letter A is the 1st letter of the alphabet, D is the 4th letter, B is the 2nd letter,
and so on. We can create the following letter–number correspondence:
Letter Number
A1
D4
Add 3.
B2
Subtract 2.
E5
Add 3.
C3
Subtract 2.
F6
Add 3.
D4
Subtract 2.
The numbers in the sequence 1, 4, 2, 5, 3, 6, 4,...alternate in size. They change
from smaller to larger, to smaller, to larger, and so on.
We see that 3 is added to the first number to get the second number. Then 2 is
subtracted from the second number to get the third number. To get successive
numbers in the sequence, we alternately add 3 to one number and then subtract 2
from that result to get the next number.
Applying this pattern, the next number in the given numerical sequence would
be 4 3, or 7. The next letter in the original sequence would be G, because it is the
7th letter of the alphabet.





 






Self Check 3
Find the next letter in
the sequence B, G, D, I,
F, K, H,....
Now TryProblem 19
Self Check 4
Find the next shape in the
sequence below.
Now TryProblem 23
,,,

...

EXAMPLE (^4) Find the next shape in the sequence below.
StrategyTo find the next shape in the sequence, we will focus on the changing
positions of the dots.
WHYThe star does not change in any way from term to term.
Solution
We see that each of the three dots moves from one point of the star
to the next, in a counterclockwise direction. This is a circular
pattern.The next shape in the sequence will be the one shown here.
,,,

...