8.4617....
Hope this helped you :)
Answer:
A. Division property of inequality.
Step-by-step explanation:
Let be
, we proceed to show the appropriate procedure to step 4:
1)
Given
2)
Compatibility with multiplication/Existence of multiplicative inverse/Associative property/Modulative property/Result. (Division property of inequality)
In consequence, the division property of inequality which states that:
. If
, then:
![a> b\,\longrightarrow a\cdot c > b\cdot c \,\lor\, a](https://tex.z-dn.net/?f=a%3E%20b%5C%2C%5Clongrightarrow%20a%5Ccdot%20c%20%3E%20b%5Ccdot%20c%20%5C%2C%5Clor%5C%2C%20a%3Cb%20%5Clongrightarrow%20a%5Ccdot%20c%20%3C%20b%5Ccdot%20c)
But if
, then:
![a> b\,\longrightarrow a\cdot c < b\cdot c \,\lor\, a b\cdot c](https://tex.z-dn.net/?f=a%3E%20b%5C%2C%5Clongrightarrow%20a%5Ccdot%20c%20%3C%20b%5Ccdot%20c%20%5C%2C%5Clor%5C%2C%20a%3Cb%20%5Clongrightarrow%20a%5Ccdot%20c%20%3E%20b%5Ccdot%20c)
Hence, correct answer is A.
Answer:
The 53rd term of this arithmetic sequence is -805.
Step-by-step explanation:
The general rule of an arithmetic sequence is the following:
![a_{n+1} = a_{n} + d](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20a_%7Bn%7D%20%2B%20d)
In which d is the common diference between each term, that is,
.
To find the nth term of the sequence, this equation can be written as:
![a_{n} = a_{1} + (n-1)d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29d)
27,11, -5
So ![a_{1} = 27, a_{2} - a_{1} = 11 - 27 = -16[/tex[tex]a_{n} = a_{1} + (n-1)d](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2027%2C%20a_%7B2%7D%20-%20a_%7B1%7D%20%3D%2011%20-%2027%20%3D%20-16%5B%2Ftex%3C%2Fp%3E%3Cp%3E%5Btex%5Da_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29d)
![a_{53} = a_{1} + (52)d = 27 + 52*(-16) = -805](https://tex.z-dn.net/?f=a_%7B53%7D%20%3D%20a_%7B1%7D%20%2B%20%2852%29d%20%3D%2027%20%2B%2052%2A%28-16%29%20%3D%20-805)
The 53rd term of this arithmetic sequence is -805.
You will get r= 21/12 but you have to simplify to get R=7/4 or R=1.75