following patterns of 3 9 4 12 7

Question

Following patterns number 2 9 4 12 7

Answer 1

Fernando,

When confronting a series such as this, usually you start by trying to make a pattern by the differences between successive terms. Thus 3, 9, 4, 12, 7,  becomes +6, -5, +8, -5. The problem from this point lies in the unfortunate fact that an infinite number of patterns connect any (finite) small series of numbers. Thus, while you could say that this has the form: Start at 3; add n=6, subtract 5 (constantly), add n+2=8, subtract 5, (add n+4=10; subtract 5, etc.). Or you could go into more offbeat patterns, such as : start with 3, next term is x3 =9; skip 0 and take next even number beyond the 3=4; then x3=12; skip 1 and take next odd number beyond the 4 = 7; x3=21; skip 2 and take next even number beyond the 7 = 10; etc.

Really, all that limits you is your imagination. There is no "right" answer, just some that are simpler rules, and some that are more complex ones! You could mix addition, subtraction, multiplication, division; formulas involving only each successive term, or those combining more than one successive term (such as the Fibonacci numbers); things involving algebraic or geometrical ideas to generate terms, and so on.

Have fun. By the way, there are compiled patterns already worked out for such series in one of the Handbooks -- you might have fun trying to find and appreciate.

Answer 2

Hi Fernando,

Since you have given two different sequences, there is some doubt about which is the correct problem!

If the 2,9,4,12,7 sequence is used

there is a pattern of "add 7, subtract 5" repeating.

The other problem, 3,9,3,12,7, does not have such a pattern.

CORRECTION: This answer is not correct and there does not appear to be a simple pattern to answer this problem.