Given the Recursive Formula:
a1 = 5
a4 = an−1 +2
What is the common difference?
What is the initial term?
What term is this formula solving for?
What should be in place of the n-1?
a1 = 5
an = a(n-1)+2
What is the common difference? 2
What is the initial term? 5
What term is this formula solving for? a4
What should be in place of the n-1? 4-1 = 3
Yes, you're correct. In this case, the common difference is 2, the initial term is 5, the formula is solving for the term a4, and in place of n-1, you would replace it with 4-1, which is 3.
To find the common difference in a recursive formula, we need to find the difference between two consecutive terms. In this case, we are given that a4 = an−1 + 2.
To find the common difference, we need to compare two terms that are consecutive. Let's take a4 and a3 as an example:
a4 = a3 + 2
Since a3 is the term before a4, we can say a3 = a2 + 2. Similarly, a2 can be expressed as a1 + 2. Substituting these values into the equation, we get:
a4 = (a1 + 2) + 2
Simplifying further:
a4 = a1 + 4
Here, we see that the difference between consecutive terms is always 4. Therefore, the common difference in this recursive formula is 4.
Now, let's determine the initial term (a1). We are given that a1 = 5, so the initial term in this recursive formula is 5.
The recursive formula is solving for the nth term, where n represents the position of the term. In this case, the formula is solving for the nth term because it uses the general term an−1, which indicates that it is solving for the term before the nth term.
Finally, in place of n-1, you should put the position of the term minus 1. For example, if you want to find the 10th term using this recursive formula, you would substitute n-1 with 10-1, which equals 9.
The common difference is the constant added to each term to get the next term in the sequence. In this case, the common difference is 2.
The initial term, a1, is the first term in the sequence. Given in the question, a1 = 5.
The formula is solving for the nth term in the sequence. It represents a relationship between each term and the previous term.
In place of n-1, there should be a specific term number. For example, if we want to find the 5th term, we would replace n-1 with 5-1 = 4. So, in this case, a4 = a(4-1) + 2.