Given the explicit formula: a7= −12 + (n − 1)(−4)
What value should replace n?
To find the value that should replace n in the formula, we need to determine the position of the term we are interested in. In this case, we are looking for a7, which represents the 7th term in the sequence.
The explicit formula a7 = -12 + (n - 1)(-4) gives us the expression to calculate the value of the 7th term.
To find the value of n for the 7th term, we substitute the position (7) into the formula:
a7 = -12 + (7 - 1)(-4)
Simplifying further:
a7 = -12 + (6)(-4)
Evaluate the expression:
a7 = -12 + (-24)
a7 = -36
Therefore, the value that should replace n in the formula is 7.
To find the value that should replace n, we can rearrange the formula to solve for n.
a7 = -12 + (n - 1)(-4)
a7 + 12 = (n - 1)(-4)
(a7 + 12)/-4 = n - 1
[(a7 + 12)/-4] + 1 = n
Therefore, the value that should replace n would be [(a7 + 12)/-4] + 1.
To find the value that should replace n in the explicit formula, we need to know which term we are looking for. In this case, we are looking for the 7th term, which is represented by a7.
The formula given is a general formula for finding the nth term in a sequence. By substituting 7 for n in the formula, we can determine the value of the 7th term.
Let's substitute n = 7 into the formula:
a7 = -12 + (7 - 1)(-4)
Now, simplify the expression inside the parentheses:
a7 = -12 + (6)(-4)
a7 = -12 + (-24)
Finally, perform the addition:
a7 = -12 - 24
a7 = -36
Therefore, the value that replaces n in the given formula to find the 7th term is -36.