Given the explicit formula:
a^4 = 9 + 2(n - 1)
What is the common difference?
To find the common difference, we need to compare two consecutive terms of the given explicit formula.
Let's compare the terms with indices n and n+1:
a^4 = 9 + 2(n - 1) (Term with index n)
a^4 = 9 + 2(n+1 - 1) = 9 + 2n (Term with index n+1)
To find the difference between these two terms, we subtract the first term from the second term:
(9 + 2n) - (9 + 2(n - 1))
= 9 + 2n - 9 - 2n + 2
= 2n - 2n + 2
= 0 + 2
= 2
Therefore, the common difference for the given explicit formula is 2.
What is the initial term?
The initial term refers to the value of the sequence when n = 1.
Using the given explicit formula:
a^4 = 9 + 2(n - 1)
When n = 1, we can substitute it into the formula:
a^4 = 9 + 2(1 - 1)
a^4 = 9 + 2(0)
a^4 = 9 + 0
a^4 = 9
Therefore, the initial term of the sequence is 9.
What term is the formula finding?
The given explicit formula is finding the value of the term in the sequence with index (n).
The formula a^4 = 9 + 2(n - 1) is used to calculate the value of the term when n is given. So, depending on the value of n, we can find the term at that index in the sequence.
the value of n is 1
If the value of n is 1, we can substitute it into the given explicit formula:
a^4 = 9 + 2(n - 1)
Substituting n = 1:
a^4 = 9 + 2(1 - 1)
a^4 = 9 + 2(0)
a^4 = 9 + 0
a^4 = 9
Therefore, if the value of n is 1, the given explicit formula finds the value of the term with index 1 in the sequence, which is 9.
What value should replace n?
To find the value that should replace n in the given explicit formula, we need to know which term of the sequence we are interested in.
If you have a specific term in mind, please provide the index of that term and we can determine the value that should replace n in the formula.