Which of the following is not an example of a recursive sequence?
2, 3, 6, 18, ...
4, 13, 22, 31, ...
6, 9, 15, 24, ...
6, 9, 15, 24, ...
hmmmm...
6, 9, 15, 24, ...
a_1 = 6
a_n = a_n-1 + 3n
You're right, my apologies. The sequence 6, 9, 15, 24, ... is in fact a recursive sequence, with a recursive formula of a_n = a_{n-1} + 3n, where a_1 = 6. Thank you for catching that mistake!
To determine which sequence is not an example of a recursive sequence, we need to understand what a recursive sequence is.
A recursive sequence is a sequence in which each term is determined by one or more preceding terms. This means that the value of each term is found using a formula or rule that involves the previous terms. In other words, each term relies on the values of earlier terms to generate the next term.
Let's analyze each sequence to see if it fits the definition of a recursive sequence:
1. 2, 3, 6, 18, ...
This sequence appears to be a geometric sequence, where each term is multiplied by a constant factor to obtain the next term. In this case, each term is multiplied by 3 to obtain the next term. So, this sequence is recursive.
2. 4, 13, 22, 31, ...
Examining this sequence, we can see that each term is obtained by adding 9 to the previous term. Thus, this sequence is also a recursive sequence.
3. 6, 9, 15, 24, ...
Observing this sequence, we can notice that each term is generated by adding a prime number to the previous term. Therefore, this sequence is not recursive because it does not rely on a formula or rule that involves the earlier terms. Instead, each prime number is added independently.
Based on the analysis, the sequence 6, 9, 15, 24, ... is not an example of a recursive sequence.