How to write a formula for a sequence?

Question

Example sequence: 3, 6, 12, 24, 48, 96

Answer 1

The general idea is to try to come up with a function f(x) so that f(1) gives the first item in the sequence, f(2) gives the second, etc. How you get from one item to the next will usually give you a clue as to what the function will look like.

In this case, you are multiplying by 2 to get from one item the next, so something like 2^n will probably figure in the function. After a little fooling around, you should come up with f(x) = 3 * 2^(n-1) for this sequence.

Answer 2

Notice that 6 is 2*3
12 is 2*6=2*2*3=2^2*3
24 is 2*12=2*2*2*3=2^3*3
48 is 2^4*3
etc.

You get the idea, now just write that down for a general number n.

Answer 3

a sub n = 3(2)^n, n = 0 through 6

Answer 4

a_1= 3 a_n = 3*(n-1)^2