An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).
The equation for an arithmetic sequence is
![A_{n}=A_{1}+(n-1)d](https://tex.z-dn.net/?f=A_%7Bn%7D%3DA_%7B1%7D%2B%28n-1%29d)
![A_{n}](https://tex.z-dn.net/?f=A_%7Bn%7D)
is the "n-th" number in the sequence (ex: is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 47 so
![A_{1}=47](https://tex.z-dn.net/?f=A_%7B1%7D%3D47)
<span>d=-2 because the question gives you that
</span>
![A_{n}=A_{1}+(n-1)d](https://tex.z-dn.net/?f=A_%7Bn%7D%3DA_%7B1%7D%2B%28n-1%29d)
<span>
![A_{29}=47+(29-1)(-2)](https://tex.z-dn.net/?f=A_%7B29%7D%3D47%2B%2829-1%29%28-2%29)
</span><span>
![A_{29}=47+(28)(-2)](https://tex.z-dn.net/?f=A_%7B29%7D%3D47%2B%2828%29%28-2%29)
</span><span>
![A_{29}=47+-56](https://tex.z-dn.net/?f=A_%7B29%7D%3D47%2B-56)
</span><span>
![A_{29}=-9](https://tex.z-dn.net/?f=A_%7B29%7D%3D-9)
</span>
The answer is A. -9.
<u> </u>
<span>The answer is C. 158</span>
For the second one, it gives you
![A_{1}=4](https://tex.z-dn.net/?f=A_%7B1%7D%3D4)
and <span>
![A_{}=18](https://tex.z-dn.net/?f=A_%7B%7D%3D18)
You can use this to find d
</span><span>
![A_{n}=A_{1}+(n-1)d](https://tex.z-dn.net/?f=A_%7Bn%7D%3DA_%7B1%7D%2B%28n-1%29d)
</span><span>
![A_{3}=4+(3-1)d](https://tex.z-dn.net/?f=A_%7B3%7D%3D4%2B%283-1%29d)
</span><span>
![18=4+(3-1)d](https://tex.z-dn.net/?f=18%3D4%2B%283-1%29d)
</span><span>
![18=4+2d](https://tex.z-dn.net/?f=18%3D4%2B2d)
</span><span>
![14=2d](https://tex.z-dn.net/?f=14%3D2d)
</span><span>
![7=d](https://tex.z-dn.net/?f=7%3Dd)
</span>
Now you can just solve using the equation normally.
<span>
![A_{n}=A_{1}+(n-1)d](https://tex.z-dn.net/?f=A_%7Bn%7D%3DA_%7B1%7D%2B%28n-1%29d)
</span><span>
![A_{23}=4+(23-1)(7)](https://tex.z-dn.net/?f=A_%7B23%7D%3D4%2B%2823-1%29%287%29)
</span><span>
![A_{23}=4+(22)(7)](https://tex.z-dn.net/?f=A_%7B23%7D%3D4%2B%2822%29%287%29)
</span><span>
![A_{23}=4+154](https://tex.z-dn.net/?f=A_%7B23%7D%3D4%2B154)
</span><span>
![A_{23}=158](https://tex.z-dn.net/?f=A_%7B23%7D%3D158)
</span>
The answer is C. 158
Answer:
![m=\frac{-3}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-3%7D%7B5%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Slope Formula:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point (4, 3)
Point (-1, 6)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>
- Substitute [SF]:
![m=\frac{6-3}{-1-4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6-3%7D%7B-1-4%7D)
- Subtract:
![m=\frac{3}{-5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B-5%7D)
- Rewrite:
![m=\frac{-3}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-3%7D%7B5%7D)
Answer:
The area will be 834.38
Step-by-step explanation:
hope it helps..
Answer:
Ration is an ordered pair of numbers that show a comparison between two things.
Answer:
The equation would be y = x + 5, in which x is the number of weeks and y is the number of books he has.
Step-by-step explanation:
We know this because even at 0 weeks, he still has 5 books. Therefore we put this as the constant at the end. Then we can add the number of weeks since the rate is one book per week.