Given the Recursive Formula:
a1 = −8
a6 = an +5
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?
The common difference is the difference between consecutive terms in a sequence. In this case, the common difference is 5.
The initial term, or the first term in the sequence, is a1 = -8.
The formula is solving for the nth term in the sequence.
In place of the n, there should be the specific term number that the formula is solving for. For example, if we want to find the 6th term, then n would be 6.
To find the common difference, we can subtract consecutive terms in the sequence.
Given the recursive formula:
a1 = -8
a6 = an + 5
To find the common difference, we subtract a1 from a6:
a6 - a1 = (an + 5) - (-8)
= an + 5 + 8
= an + 13
The common difference is 13.
The initial term is given as a1 = -8.
The formula is solving for the term an.
In place of the "n", you would substitute the specific term you are trying to find in the sequence.
To understand the given recursive formula, let's break it down step by step:
1. The common difference:
In a recursive formula, the common difference refers to the amount added or subtracted to each term to get to the next term. However, the given recursive formula does not explicitly provide the common difference. Instead, it states that the sixth term (a6) is equal to the sum of the n-th term (an) and 5. Therefore, we cannot determine the common difference from this recursive formula alone.
2. The initial term (a1):
The initial term, also known as the first term, can be found in the recursive formula. In this case, we are given that the first term (a1) is -8.
3. The term being solved for:
The recursive formula does not explicitly state which term it is solving for. To determine the term being solved for, we need more information or context.
4. The variable replacement for n:
In the given formula, the variable n represents the term number. To find a specific term, substitute the desired term number into the formula. For example, to find the 6th term, we replace n with 6 in the formula a6 = an + 5.
To summarize:
- The common difference cannot be determined from the given recursive formula alone.
- The initial term (a1) is -8.
- The term being solved for is not specified.
- To find a specific term, replace the variable n with the desired term number in the formula.