Given the explicit formula: a7= −12 + (n − 1)(−4)
What is the common difference?
A. -12
B. -4
C. 6
D. 7
The common difference in an arithmetic sequence is the difference between each term and the previous term.
In this explicit formula, the term n is substituted as 7.
So, a7 = -12 + (7 - 1)(-4) = -12 + 6(-4) = -12 + (-24) = -36
To find the common difference, we can subtract the previous term (a6) from a7:
a7 - a6 = -36 - (-12 + (6 - 1)(-4)) = -36 - (-12 + 5(-4)) = -36 - (-12 + (-20)) = -36 - (-32) = -36 + 32 = -4
Therefore, the common difference is -4.
The correct answer is B. -4.
What is the initial term?
The initial term is the first term in the arithmetic sequence.
In the explicit formula a7 = -12 + (n - 1)(-4), we can substitute n as 1 to find the initial term:
a1 = -12 + (1 - 1)(-4) = -12 + 0 = -12
Therefore, the initial term is -12.
The correct answer is -12.
What term is the formula finding?
The formula is finding the value of the term at the position given by n.
In the given explicit formula a7 = -12 + (n - 1)(-4), the formula is finding the value of the term when n is equal to 7.
Thus, the formula is finding the 7th term in the arithmetic sequence.
Therefore, the formula is finding a7, which represents the value of the 7th term.
What value should replace n?
In the given explicit formula a7 = -12 + (n - 1)(-4), the value that should replace n depends on which term in the arithmetic sequence we want to find.
If we want to find the 7th term, then n should be replaced with 7.
Therefore, the value that should replace n is 7 in order to find the 7th term.