Define the number sequence {5n}
n1 = {3,6,9,12,15, … ) recursively�
Looks like we are adding 3 to the previous term
n1 = 3
nn+1 = nn + 3
Don't know where the {5n} comes in, are you interested in only the
nn , where n consists of multiples of 5?
Do you want the nn values multiplied by 5?
You decide.
The number sequence {5n} can be defined recursively as follows:
1. Start with n = 1.
2. The first term in the sequence is obtained by multiplying 5 with the initial value of n: 5 * 1 = 5.
3. Increment n by 1 and repeat step 2 to find the next term.
4. Continue this process indefinitely.
Based on this recursion, the number sequence {5n} recursively is {5, 10, 15, 20, 25, ...}. Each term in the sequence is obtained by multiplying 5 with the corresponding value of n.
To define the number sequence {5n} recursively, we need to identify the initial term and the recursive rule.
The initial term of the sequence is given as 3. This means that when n = 1, the value of the sequence is 3.
Next, we need to determine the recursive rule, which describes how to generate the subsequent terms of the sequence based on the current term. In this case, we can observe that each term of the sequence is obtained by multiplying the previous term by 5. So, the recursive rule for {5n} can be stated as:
For n ≥ 2, each term is found by multiplying the previous term by 5:
5n = 5 * (n-1)
Using this recursive rule, we can continue generating terms for the sequence:
When n = 2,
5n = 5 * (2-1) = 5 * 1 = 5
When n = 3,
5n = 5 * (3-1) = 5 * 2 = 10
Continuing this process, we can generate more terms for the sequence.
To summarize, the sequence {5n} recursively defined with the initial term 3 and the recursive rule 5n = 5 * (n-1). The first few terms of the sequence are 3, 5, 10, 15, ...