Note that when you ask a question you need to specify what you do and do not understand about the situation.
could you explain inductive and deductive reasoning?
Inductive reasoning is basically reasoning from a pattern you think will repeat itself. For example, it didn't rain yesterday or the day before, and it has only rained once in the last 18 days. We expect that it won't rain tomorrow either, but that's an inductive conclusion.
Deductive reasoning employs the rules of logic to draw specific conclusions from general statements. For example if my name comes before your name in the alphabet, and your name comes before Fred's name, then my name comes before Fred's name. That is a deductive conclusion, not based on specific instances and patterns but on a general rule of logic.
would you work a problem using the method of successive differences?
Suppose you have the sequence
2 9 28 65 126 217 ...
The differences of this sequence are
7 19 37 61 91 ...
The differences of this sequence are
12 18 24 30 ... . Perhaps you see the pattern in this sequence, but if not the differences of this sequence are
6 6 6 ... .
Assuming that these differences continue, the next number in 12 18 24 30 ... would be obtained by adding 6 to get 36.
Then since this sequence gives the differences in 7 19 37 61 91 ... the next number in this sequence would be obtained by adding 36, to get 127.
Finally since this sequence gives the differences in the original sequene 2 9 28 65 126 217 ... the next number in this sequence would be obtained by adding 127, to get 344.
Donna is taller than david but shorter than bill. dan is shorter than bob. what is the first letter in the name of the tallest person?
Bill is taller than Donna and therefore taller than David.
Bob is taller than Dan.
So someone whose first name begins with B is taller than Donna, David and Dan.
Therefore either Bob or Bill is the tallest.
The name of the tallest thus starts with B.
This is an example of deductive reasoning.