Find a recursive rule for the sequence 3, 6, 12, 24, …
I can't decide if it's
a sub n= (2)n times sub n-1
or
a sub n= 1/2 times sub n-1
To find the recursive rule for the sequence 3, 6, 12, 24, ..., you need to observe the pattern and understand how each term relates to the previous term.
Looking at the sequence, notice that each term is obtained by doubling the previous term. So, you can express the recursive rule as follows:
a[sub]n[/sub] = 2 * a[sub]n-1[/sub]
Here's how you can derive this rule:
- The first term is 3, which we denote as a[sub]1[/sub].
- The second term is obtained by multiplying the first term (3) by 2: a[sub]2[/sub] = 2 * a[sub]1[/sub] = 2 * 3 = 6.
- The third term is obtained by doubling the second term: a[sub]3[/sub] = 2 * a[sub]2[/sub] = 2 * 6 = 12.
- The fourth term is obtained by doubling the third term: a[sub]4[/sub] = 2 * a[sub]3[/sub] = 2 * 12 = 24.
Following this pattern, you can see that each term is twice the previous term. Therefore, the recursive rule is a[sub]n[/sub] = 2 * a[sub]n-1[/sub].
first, you might fix your typos. Your formulas are bogus.
Next, you can easily see that the values get bigger and bigger, so the 1/2 formula can't be right.
Your first try is right, but should be written
a(1) = 3
a(n) = 2*a(n-1) for n > 1