We're doing sequence things in class how do I find the general term of this set (4,8,6,16,8,32,10,64). The answer must be in an equation.
The next in the sequence would be 12, 128. I thought the answer was f(x) = 2x but that doesn't account for 6,8,10
Looks to me like
Tn = 2n+2 if n is odd
Tn = 4*2^(n/2) if n is even
Hmmm. Better make that
Tn = n+3 if n is odd
To find the general term of a sequence, we need to observe the pattern and determine a formula that relates the position of a term in the sequence (the index) to the value of that term. Let's break down the given sequence (4, 8, 6, 16, 8, 32, 10, 64) to identify the pattern:
Notice that the odd-indexed terms in the sequence (1st, 3rd, 5th, 7th) follow the pattern: 4, 6, 8, 10. These terms are increasing by 2 with each step.
Now, let's examine the even-indexed terms (2nd, 4th, 6th, 8th): 8, 16, 32, 64. These terms are doubling with each step.
So, to find the general term, we can express it as a piecewise function. Let's call the index of the term n:
If n is even, the term can be represented as 2^(n/2).
If n is odd, the term can be represented as (n+2)/2.
Therefore, the general term of the given sequence can be written as:
f(n) = (n+2)/2 if n is odd
f(n) = 2^(n/2) if n is even
For example:
f(1) = (1+2)/2 = 3/2 = 1.5
f(2) = 2^(2/2) = 2^1 = 2
f(3) = (3+2)/2 = 5/2 = 2.5
f(4) = 2^(4/2) = 2^2 = 4
By plugging in different values for n, you can find the corresponding terms in the sequence.