Answer:
The 53rd term of this arithmetic sequence is -805.
Step-by-step explanation:
The general rule of an arithmetic sequence is the following:

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:

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)

The 53rd term of this arithmetic sequence is -805.
Answer:
83746+4747+48484=3943848343
Step-by-step explanation:
Easy
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
2x-y=6;5x+10y=-10. -y=-2x+6. -y/-1=-2x+6/-1. y=2x-6. 5x+10y=-10. 5x+10(2x-6)=-10. 25x-60=-10. 25x=50. 25x/25=50/25. y=2x-6. y=(2)(2)-6. y=-2. Therefore, x=2 and y=-2
It was the English Scientist Sir Isaac Newton.