A(n) = a₁.(r)ⁿ⁻¹, where a₁ = 1st term, r= common ratio and n, the rank
In the formula given a₁ = 5, r = 3/2 and n = 6 (we have to find the 6th term value).
a₆ = 5.(3/2)⁶⁻¹ = 5.(3/2)⁵ = 1215/32 (answer C)
Yes. The two theorems are equivalent statements given that the fundamental theorem of calculus is true.
so we have a table of values, with x,y coordinates, so let's use any two of those points to get the slope of the table and use the point-slope form to get its equation
![~\hspace{2.7em}\stackrel{\textit{let's use}}{\downarrow }\qquad \stackrel{\textit{and this}}{\downarrow }\\\begin{array}{|lr|r|r|r|r|}\cline{1-6}x&0&1&2&3&4\\y&-1&3&7&11&15\\\cline{1-6}\end{array}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{15})](https://tex.z-dn.net/?f=~%5Chspace%7B2.7em%7D%5Cstackrel%7B%5Ctextit%7Blet%27s%20use%7D%7D%7B%5Cdownarrow%20%7D%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Band%20this%7D%7D%7B%5Cdownarrow%20%7D%5C%5C%5Cbegin%7Barray%7D%7B%7Clr%7Cr%7Cr%7Cr%7Cr%7C%7D%5Ccline%7B1-6%7Dx%260%261%262%263%264%5C%5Cy%26-1%263%267%2611%2615%5C%5C%5Ccline%7B1-6%7D%5Cend%7Barray%7D%5C%5C%5C%5C%5B-0.35em%5D%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B3%7D%29%5Cqquad%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B15%7D%29)
Remark
The quick answer is C does not represent a function. It has two y values for x = 2. These two points are (2,1) and (2,3). That eliminates C. No x can have 2 y values and be called a function. A function can have many x vales for a single y and still be a function.
A has all different x values, so it could be classed as a function. There are no values where x has more than 1 y value.
B also has all different x values. It too is a function.
Answer
A and B are both functions. C is not.
D <<<<< Answer
The correct answer among the choices listed above is the second option. <span>The following system of equations is equivalent. This is because when written in the same form, one equation will yield to the same equation as the other.
</span>y = -1/3x +2/3
<span>2x + 6y = 4
</span>6y = 4 - 2x
y = 2/3 - 1/3x
<span>y = -1/3x +2/3 </span>
