The answer is Vertical angles are equal.
B my dud yayayyayayyayayyayay
Answer:
<u>There are 17 terms in the sequence</u>
Step-by-step explanation:
<u>Arithmetic Sequence
</u>
An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:
![a_n=a_1+(n-1)r](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29r)
Where an is the nth term, a1 is the first term, and r is the common difference.
In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:
![\displaystyle n=1+\frac{a_n-a_1}{r}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%3D1%2B%5Cfrac%7Ba_n-a_1%7D%7Br%7D)
We need to express r as an improper or proper fraction:
![\displaystyle r=-2\frac{1}{4}=-2-\frac{1}{4}=-\frac{9}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D-2%5Cfrac%7B1%7D%7B4%7D%3D-2-%5Cfrac%7B1%7D%7B4%7D%3D-%5Cfrac%7B9%7D%7B4%7D)
Substituting:
![\displaystyle n=1+\frac{-23-13}{-\frac{9}{4}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%3D1%2B%5Cfrac%7B-23-13%7D%7B-%5Cfrac%7B9%7D%7B4%7D%7D)
![\displaystyle n=1+\frac{-36}{-\frac{9}{4}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%3D1%2B%5Cfrac%7B-36%7D%7B-%5Cfrac%7B9%7D%7B4%7D%7D)
![\displaystyle n=1+36*\frac{4}{9}=17](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%3D1%2B36%2A%5Cfrac%7B4%7D%7B9%7D%3D17)
n=17
There are 17 terms in the sequence