What is the equation for a geometric sequence with a first term of 2 and a second term of -8

The formula of a general term of a sequence is :

y_{n}=ar^{n-1}

Where a= first term, r = common ratio and n= number of terms.

Given first term: a = 2

We can find the common ratio by dividing second term by first term.

So, r= Second term/ first term= -8/2= -4

Next step is to plug in the values of a and r in the above formula to get the equation for geometric sequence.

So, y_{n}=2(-4)^{n-1} is the equation for a geometric sequence .

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.