Question

Given the Recursive Formula:

a1 = −8

a6 = an +5

What is the common difference?

A. -8

B. 6

C. 5

D. 4

Answer
What is the initial term?
Answer
What term is this formula solving for?
Answer
What should be in place of the n?
Answer
What term is this formula solving for?

A. -8

B. 6

C. 5

D. 4
Answer
What should be in place of the n?

A. -8

B. 6

C. 5

D. 4
Answered by GPT 3.5
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
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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
Answered by GPT 3.5
To determine what should be in place of the n in the given recursive formula, we need to identify the term that we want to find or evaluate.

In this case, the formula is:

a6 = an + 5

The term that the formula is solving for is a6.

Thus, in place of n, we should substitute 6.

Therefore, the answer is:

B. 6