Given the explicit formula: a7= −12 + (n − 1)(−4)
What is the common difference?
What is the initial term?
What term is the formula finding?
What value should replace n?
The common difference is -4.
The initial term is a7, which is -12.
The formula is finding the nth term of the sequence.
The value that should replace n depends on the specific term you want to find in the sequence.
To find the common difference, we need to look at the formula. The common difference is the coefficient of the term (n - 1). In this case, the coefficient is -4. Therefore, the common difference is -4.
The initial term, also known as the first term, can be found by evaluating the formula for n=1. Plugging n=1 into the formula gives us a7 = -12 + (1 - 1)(-4) = -12. Therefore, the initial term is -12.
The formula is finding the term with the subscript 7, which is denoted as a7. So, the formula is finding the 7th term.
To determine the value that should replace n, we need to look at the given formula again. The formula states a7 = -12 + (n - 1)(-4). As we want to find the term with the subscript 7, we substitute 7 into the formula for n. Therefore, the value that should replace n is 7.
To find the common difference in the explicit formula, we can compare two consecutive terms.
In this case, the formula is a7 = -12 + (n - 1)(-4).
Let's compare a7 and a6:
a7 = -12 + (n - 1)(-4)
a6 = -12 + (n - 1 - 1)(-4) = -12 + (n - 2)(-4)
The common difference is the difference between a7 and a6, which is:
(a7) - (a6) = (-12 + (n - 1)(-4)) - (-12 + (n - 2)(-4))
= (-12 - (-12)) + ((n - 1) - (n - 2))(-4)
= -4
Therefore, the common difference is -4.
To find the initial term or the first term in the sequence, we can substitute n = 1 into the formula.
Using n = 1, the formula becomes:
a1 = -12 + (1 - 1)(-4)
= -12
So, the initial term is -12.
The formula is finding the term a7, which means it is finding the seventh term in the sequence.
To know what value should replace n, we need more information, such as the specific term we want to find in the sequence.