What is the next number in the sequence: 9, 3, 1, 1/3,...?.....I have alot of these questions with different sequence numbers how do I determine the the squence for each without spending alot of time on one question?

Question

heisenberg · Answer

These types of questions are all about determining patterns between the numbers. There is no "go-to" method to doing so, but a good start is to compare each number with the previous number and see any relations.

heisenberg · Answer

here we can see that it goes: 9, 3...

already i know that 9 / 3 = 3, and also $$\sqrt(9) = 3$$

heisenberg · Answer

moving on, I see: 3, 1...

well the sqrt(3) != 1, but 3 / 3 = 1

heisenberg · Answer

(!= means does not equal)

heisenberg · Answer

I'm starting to see that each number is just the previous divided by 3. the remaining numbers confirm this.

so if i have:
$$\frac{1}{3} / 3 = \frac{1}{3} * \frac{1}{3} = \frac{1}{9}$$

anonymous · Answer

in problems like this one how will I know to add, subtract, divide..etc to figure out how the sequence is going without having to use every number to get to the right one

heisenberg · Answer

You'll never really know which to use, but the idea is to eyeball the numbers and play around. The whole goal is to try and detect patterns.

Like I did up there, examine the relationship between two consecutive numbers. Then take any of those that worked and try them on another pair.

anonymous · Answer

Ok....very helpful thank you!