Answer:
n = 10 -> the 10th term has the value - 25
Step-by-step explanation:
The nth term of an arithmetic sequence can be determined by the formula
[tex]a_n = a_1 + d(n - 1)[/tex]
where
[tex]\text{$a_n$ = nth term\\}\\a_1 = \text{first term}\\d = \text{common difference- the constant difference between successive terms}\\n = \text{number of terms}[/tex]
The sequence - 7, - 9, -11 has first term aₙ = - 7 and common difference d = -2
We are given the nth term as -25 and asked to find n
Plugging in knowns we get
- 25 = - 7 +(-2)(n-1)
-25 = -7 - 2(n - 1)
-25 = -7 -2n + 2 open brackets
-25 = -5 - 2n simplify
-25 + 5 = -5 + 5 - 2n add 5 both sides
-20 = -2n
Switch sides:
-2n = -20
Divide by - 2:
-2n/-2 = -20/-2
n = 10
After identifying the common difference in the arithmetic sequence, the formula an = a1 + (n - 1)d was used to calculate n for an = -25. According to the calculations, n should be 10, which is not one of the provided options. So the correct answer is none of the above options.
To find the position n for the nth term an = -25 in the given arithmetic sequence, we first need to identify the common difference d. Looking at the sequence -7, -9, -11, we can see that the common difference between each term is -2 (each term is 2 less than the previous one).
Using the formula for any term in an arithmetic sequence, an = a1 + (n - 1)d, where a1 is the first term and d is the common difference, we can set up the equation for the nth term as follows: -25 = -7 + (n - 1)(-2)
This simplifies to: -18 = (n - 1)(-2)
Dividing both sides by -2 gives us: 9 = n - 1
Adding 1 to both sides of the equation, we find: n = 10
Since 10 is not one of the answer choices provided. Hence the correct answer is none of the above options.