Given the explicit formula: a5= 8 + (5 − 1)3
What is the common difference?
A. 5
B. 8
C. 4
D. 3
The common difference is the value that is added (or subtracted) to each term to get to the next term in the arithmetic sequence.
In the given explicit formula, the first term is 8 and the second term is (5 - 1)3 = 12.
To get from the first term (8) to the second term (12), we need to add 4.
Therefore, the common difference is 4.
C. 4
What is the initial term?
A. 5
B. 8
D. 3
The initial term, also called the first term or the starting term, is the value of the first term in the arithmetic sequence.
In the given explicit formula, the first term is stated as a5, which means it is the fifth term in the sequence.
Since we are given the formula a5 = 8 + (5 - 1)3, we can calculate the value of the fifth term by substituting 5 into the formula:
a5 = 8 + (5 - 1)3
= 8 + (4)3
= 8 + 12
= 20
Therefore, the value of the fifth term (a5) is 20.
So, the initial term (first term) is not provided in the given explicit formula. The options A, B, and D are all incorrect.
What is the initial term?
A. 5
B. 8
C. 3
Apologies for the previous response. It seems I made an error in my explanation.
The explicit formula a5= 8 + (5 − 1)3 tells us the value of the fifth term (a5) in the arithmetic sequence.
To find the initial term, we need to determine the value of the first term in the sequence.
The formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n - 1)d
Where:
an is the nth term of the sequence,
a1 is the first term of the sequence,
n is the position of the term in the sequence, and
d is the common difference.
From the given explicit formula (a5= 8 + (5 − 1)3), we can deduce that the fifth term (a5) is equal to:
a5 = a1 + (5 - 1)d
Since the fifth term (a5) is given as 8 + (5 − 1)3, we have:
8 + (5 - 1)3 = a1 + (5 - 1)d
Simplifying the left side of the equation:
8 + 4 * 3 = a1 + 4d
20 = a1 + 4d
We have the equation 20 = a1 + 4d, which gives us the relation between the initial term (a1) and the common difference (d).
To determine the value of the initial term (a1), we need more information or another equation. Unfortunately, the provided explicit formula does not give us enough information to calculate the initial term.
Therefore, the correct answer is: None of the options (A, B, or C) can be determined from the given explicit formula.
What term is the formula finding?
A. 5
B. 8
C. 3
In the given explicit formula, a5 = 8 + (5 − 1)3, the subscript "5" indicates that the formula is finding the value of the fifth term in the sequence.
Therefore, the term that the formula is finding is:
A. 5