Question

How do I use inductive reasoning to predict the next three numbers in the pattern 9,11,13,15,17

Answer 1

You inspect the series that you have, very carefully.

-- You notice that 9 was increased by 2 to get 11.
-- You notice that 11 was increased by 2 to get 13.
-- You notice that 13 was increased by 2 to get 15.
-- You notice that 15 was increased by 2 to get 17.

By now, it begins to dawn on you.  You say to yourself  "Self !  I'll just bet
that each term has to be increased by 2 in order to get the next term."

Acting on that assumption, you set out on your flight of prediction:

-- You take the last term, 17, increase it by 2,and get 19.

-- You take the new term that you have created, 19,
increase it by 2, and get 21.

-- You take the 2nd new term that you have created, 21,
increase it by 2, and get 23.

Now you have the three new terms, and that's all you were asked for.
But you're just getting warmed up.  Nothing can stop you now.

25,  27,  29,  31,  33,  35,  37,  39,  41,  43,  45,  47,  49, 
51,  53,  55,  57,  59,  61,  63,  65,  67,  69,  71,  73,  75, 
77,  79,  81,  83,  85,  87,  89,  91,  93,  95,  97,  99,  101

Suddenly, you stop !   You just realized that this is not the ONLY
possible pattern that would produce the same first 5 numbers.

Answer 2

Realize that each bumber goes up by 2 more. So you are looking at the relationships between the numbers