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 for a sequence is defined as the difference between any two consecutive terms.
In this case, the common difference is given as 5 since a6 = a(n-1) + 5.
The initial term a1 is given as -8.
The given formula is solving for the term an.
In place of n, any positive integer greater than or equal to 1 should be substituted to find the desired term in the sequence.
To find the common difference of a sequence, we need to find the difference between any two consecutive terms. In the given recursive formula, we have the base case a1 = -8 and the recursive step a6 = an + 5.
To find the common difference, we can subtract a6 from an. Since a6 = an + 5, we can rewrite it as:
an = a6 - 5
Now, we can substitute the values of a6 and a1 into this equation:
a1 = a6 - 5
-8 = a6 - 5
By solving this equation, we can find the value of a6:
a6 = -8 + 5
a6 = -3
Now, we can substitute this value of a6 into the equation for the common difference:
an = a6 - 5
an = -3 - 5
an = -8
Therefore, the common difference for this sequence is -8.
The initial term can be found from the base case, which is given as a1 = -8. So, the initial term is -8.
This recursive formula is not explicitly solving for a specific term in the sequence. However, given that a1 is given and the formula a6 = an + 5 is provided, we can find the value of the term a6 using the formula.
To fill in the placeholder for "n" in the recursive formula, we need to know which term we are trying to find. If we want to find the value of term a6, we can substitute n = 6 into the formula:
a6 = a6 + 5
Similarly, if we want to find the value of any other term in the sequence, we would substitute the corresponding value of n.