number patterns?

Question

What is the rule for:
3, 4, 6, 10, 18

I tried it for like 17 times and i still don't get it !
Help!!!

Answer 1

Take each number, multiply by two, and then subract two.

3*2 - 2 = 4
4*2 - 2 = 6
6*2 - 2 = 10
10*2 - 2 = 18

edit: I'm sure that the two possible answers are related. I would also get 34, then 66, then 130 as the next numbers in the sequence. It has to do with the fact that it started with three. If we had started at 2, then my system would always yield 2 every time, but you guys wouldn't. I think both are acceptable, although I will admit that the other method is more interesting.

Answer 2

The sequence is basically 2 more than a power of 2.
f(n) = 2^(n-1) + 2

f(1) = 1 + 2 = 3
f(2) = 2 + 2 = 4
f(3) = 4 + 2 = 6
f(4) = 8 + 2 = 10
f(5) = 16 + 2 = 18
f(6) = 32 + 2 = 34
f(7) = 64 + 2 = 66
f(8) = 128 + 2 = 130

The difference between terms is the next power of 2 (1, 2, 4, 8, etc.) You can show this by subtracting f(n+1) and f(n) ---> 2^n + 2 - 2^(n-1) - 2 = 2^n - 2^(n-1) = 2^(n-1)

You can also define each term with a relationship to the prior term:
f(n+1) = f(n) * 2 - 2 --> double and subtract 2

Again you can show this for f(n) and f(n+1):
f(n) = 2^(n-1) + 2
f(n+1) = f(n) * 2 - 2
f(n+1) = (2^(n-1) + 2) * 2) - 2
f(n+1) = 2^n + 4 - 2
f(n+1) = 2^n + 2

Or you could say:
f(n+1) = ( f(n) -1 ) * 2 --> subtract 1 and double

Again you can show this for f(n) and f(n+1):
f(n) = 2^(n-1) + 2
f(n+1) = (f(n) - 1) * 2
f(n+1) = ((2^(n-1) + 2) - 1) * 2
f(n+1) = (2^(n-1) + 1) * 2
f(n+1) = 2^n + 2

There are lots of ways to get there but the sequence is still the same:

3, 4, 6, 10, 18, 34, 66, 130, 258, 514, 1026, etc.

In other words, all the people above are correct. You can define the sequence absolutely as I have shown, or recursively based on the prior term.

Answer 3

First, look at the difference between each term

3, 4, 6, 10, 18

The difference between the next and the previous term is by:
1, 2, 4, 8

Now, the relationship between all these difference is
2^0, 2^1, 2^2, 2^3

So, you can predict the next one will be increased by 2^4, which is, so

3, 4, 6, 10, 18, 34, ...

Answer 4

Get the difference of the first two numbers, so 4-3=1.
Multiply it by two. 1*2=2
Add it to the second number. 4+2=6
So your numbers are now 3,4,6.
Get the difference of the last two numbers and multiply it by two, etc.
6-4=2
2*2=4
6+4=10 {3,4,6,10}
10-6=4
4*2=8
10+8=18 {3,4,6,10,18}

Answer 5

3 + 2^0 = 4

4 + 2^1 = 6

6 + 2^2 = 10

10 + 2^3 = 18

Answer 6

multiple by 2

3 to 4 = 1*2=2
4 to 6 =........2*2=4
6 to 10=..............4*2=8
10 to 18 =..................8*2= 16 and so on

Answer 7

The first poster's answer makes sense, but mine seems just as logical: add 1, add 2, add 4, add 8, add 16, etc., doubling the amount each time. Heh, two answers... bad problem. :)

Answer 8

add 1
add 2
add 4
add 8

so the next numbers will be 34, 66
add 16, add 32