This is what I read once and felt gr8 abt tehse ques
Mathematically speaking, problems like this are impossible. Literally!
That's because there is no restriction on what might come next in a
sequence; ANY list of numbers, chosen for no reason at all, forms a
sequence. So the next number can be anything.
A question like this is really not a math question, but a psychology
question with a bit of math involved. You are not looking for THE
sequence that starts this way, but for the one the asker is MOST
LIKELY to have chosen - the most likely one that has a particularly
simple RULE. And there is no mathematical definition for that.
If you just wanted _a_ sequence that starts this way, but can be
defined by _some_ mathematical rule, there is a technique that lets
you find an answer without guessing. This is called "the method of
finite differences," and you can find it by searching our site (using
the search form at the bottom of most pages) for the phrase. It
assumes (as is always possible) that the sequence you want is defined
by a polynomial, and finds it. Sometimes this is what the problem is
really asking for.
But often, especially when many terms are given, there is a much
simpler rule that is not of polynomial form. Then you are being asked
to use your creativity to find a nice rule. Sometimes starting with
finite differences gives you a good clue, even if you don't end up
with a polynomial; just seeing a pattern in the differences can
reveal something about the sequence. Other times it is helpful to
factor the numbers, or to look at successive ratios. Here you are
doing a more or less orderly search, in order to find something that
may not turn out to be orderly.
Some puzzles like this are really just tricks. The "rule" may be that
the numbers are in alphabetical order, or that each number somehow
"describes" the one before, or even that they are successive digits
of pi. In such cases, you have to ignore all thoughts of rules and
orderly solutions, and just let your mind wander. This is sometimes
called "lateral thinking," and it's entirely incompatible with
"formal methods"!
eg try this which is very similar to one ques posted in XLRI paper
9545864877..
the ques was what are the next 4 digits..
Linear Mode
