Given the Recursive Formula:
a1 = −8
a6 = an +5
What is the common difference?
A. -8
B. 6
C. 5
D. 4
To find the common difference, we subtract consecutive terms in the sequence.
a6 = an + 5
We are given a6 = a1 + 5, so we can substitute this in:
a1 + 5 = a1 + 5
Notice that a1 cancels out on both sides.
5 = 5
Since this equation is true, we know that a1 = a6 + 5 holds for any value of a1.
Therefore, the common difference is 5.
Answer: C. 5
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 = -8.
Therefore, the initial term is -8.
What term is this formula solving for?
The given recursive formula does not explicitly define the term it is solving for; it only provides a relationship between terms in the sequence.
From the given information, we can deduce a6 = an + 5, which means the formula is solving for the term a6.
What should be in place of the n?
In the given recursive formula, the variable n represents the position or index of the term in the sequence.
Since we are given that the term a6 is being defined by the formula an + 5, we can conclude that the value of n in this case is 6.
Therefore, in place of the n, we should substitute 6 in the formula.
What term is this formula solving for?
A. -8
B. 6
C. 5
D. 4
Apologies for the confusion in my previous response.
To determine which term the given formula is solving for, we need to examine the formula itself, which is:
a6 = an + 5
In this formula, the term being solved for is a6.
Therefore, the correct answer is:
A. -8
What should be in place of the n?
A. -8
B. 6
C. 5
D. 4