A recursive formula is a function of the previous term. The "an-1" is the term that comes before "an".
an arithmetic sequence just adds or subtracts the same number (common difference, d) between terms. looking at the recursive formula it is -9
-35, -44, -53, -62, .....
The explicit formula is a function of the terms place "n" in the sequence. This is written as :
an = a1 + d(n-1)
fill in
a1 = -35 and d = -9
an = -35 - 9(n-1)
expand to
an = -35 - 9n + 9
an = -26 - 9n
Answer:
Step 3 they took the square root incorrectly
Step-by-step explanation:
5 ( x-2)^2 +6 = 86
Subtract 6 from each side
5 ( x-2)^2 +6 -6= 86-6
5 ( x-2)^2 = 80
Divide each side by 5
5 ( x-2)^2 /5 = 80/5
(x-2)^2 = 16
Take the square root of each side
sqrt((x-2)^2) = ±sqrt(16)
x-2 = ±4
Answer:
18 ft.
Step-by-step explanation:
While you don't have the table provided, this is still a relatively simple problem to solve.
As we know, there are 3 feet per 1 yard (this can be written as 3 ft. = 1 yd. if that's easier to comprehend). So, if we're trying to find how many feet are in 6 yards, you'll write out your equation as 3*6=?. To find what ? is, you'll do the multiplication: 3*6-18.
So, with this, there are 18 feet in 6 yards.
Let number of cranberries did Carissa eat on Thanksgiving Thursday = x
Given that she ate 7 cranberries on each following day so that seems she is following arithmetic sequence.
Whose first term is a = x
common difference d = 7
Given that on following Wednesday night, she had eaten a
total of 161 cranberries for the whole week.
Wednesday means on 7th day from thanksgiving day.
Then sum of 7 terms of the sequence is 161
S7=161
Sum of arithmetic sequcen is given by formula:
![S_n=\frac{n}{2}(2a+(n-1)d)](https://tex.z-dn.net/?f=%20S_n%3D%5Cfrac%7Bn%7D%7B2%7D%282a%2B%28n-1%29d%29%20)
![S_7=\frac{7}{2}(2*x+(7-1)*7)](https://tex.z-dn.net/?f=%20S_7%3D%5Cfrac%7B7%7D%7B2%7D%282%2Ax%2B%287-1%29%2A7%29%20)
![161=\frac{7}{2}(2x+6*7)](https://tex.z-dn.net/?f=%20161%3D%5Cfrac%7B7%7D%7B2%7D%282x%2B6%2A7%29%20)
![161=\frac{7}{2}(2x+42)](https://tex.z-dn.net/?f=%20161%3D%5Cfrac%7B7%7D%7B2%7D%282x%2B42%29%20)
![161*2=7(2x+42)](https://tex.z-dn.net/?f=%20161%2A2%3D7%282x%2B42%29%20)
![322=14x+294](https://tex.z-dn.net/?f=%20322%3D14x%2B294%20)
322-294=14x
28=14x
2=x
Hence Carissa ate 2 cranberries on Thanksgiving Thursday.
Now we have to find the number of day on which Carissa will eat 499 cranberries.
So we will use nth term formula
![t_n=a+(n-1)*d](https://tex.z-dn.net/?f=%20t_n%3Da%2B%28n-1%29%2Ad%20)
![499=2+(n-1)*7](https://tex.z-dn.net/?f=%20499%3D2%2B%28n-1%29%2A7%20)
![499=2+7n-7](https://tex.z-dn.net/?f=%20499%3D2%2B7n-7%20)
![499=7n-5](https://tex.z-dn.net/?f=%20499%3D7n-5%20)
![499+5=7n](https://tex.z-dn.net/?f=%20499%2B5%3D7n%20)
![504=7n](https://tex.z-dn.net/?f=%20504%3D7n%20)
72=n
Hence final answer is 72nd day.
B because 6x4=24 and trust me pls