Given the Recursive Formula:
a1 = 5
a4 = an−1 +2
What is the common difference?
A. 5
B. 2
C. 3
D. 4
To find the common difference of a recursive formula, we need to find the difference between any two consecutive terms.
In this case, we are given that a4 = an−1 + 2.
This means that the fourth term (a4) is equal to the previous term (an−1) plus 2.
The common difference can be found by subtracting the previous term from the fourth term:
a4 - an−1 = 2.
Since we are given that the fourth term (a4) is equal to the previous term (an−1) plus 2, we can substitute a4 for (an−1 + 2):
(a4) - an−1 = 2.
Simplifying further, we get:
2 = 2.
Since the equation is true, this means that the common difference is 2.
Therefore, the answer is B. 2.
What is the initial term?
The initial term, also known as the first term, is denoted as a1 in the recursive formula.
In this case, we are given that a1 = 5.
Therefore, the initial term is 5.
What term is this formula solving for?
The formula is solving for the term a4.
What should be in place of the n-1?
In the given recursive formula, the term "an−1" represents the term before the term being solved for, which is denoted as "an".
In this case, since we are solving for the term "a4", the term before "a4" would be "a3".
Therefore, the correct expression should be "a3 + 2" instead of "an−1 + 2".