#1**0 **

A.) Geometric, sum of all terms is gotta be either -infinite, or all of that added up, I don't have the patience to work that out.

B.) No.

C.) 1+2+4+8+16+32+64+128+256=511, so n=9

D.) So uhh, I'm confused, but I think I get it. It's 4550, because 650+600+550+450...+150+100+50+0=4550

Someone smarter than me can do B.) because I'm lazy.

Yay!

Varxaax Mar 13, 2021

#5**0 **

A) geometric sequence, and the sum is just \(-\frac{512+256+128+\dots+2+1}{512} = \boxed{-\frac{1023}{512}}\).

(notice that 1023 is one smaller than 1024, which is 2^10)

B) Idk if my solution is even close to optimal, but here it is:

Let the common difference be x. Then,

\((35-6x)+(35-5x)+(35-4x)+(35-3x)+(35-2x)+(35-x)+(35)+(35+x)=220\\ 8(35) - 20x=220\\ -20x=-60\\ \boxed{x=3}\)

The common difference is therefore equal to 3

The first term is just \(35-6(3)=\boxed{17}\)

varvaax lmao I'm not that good :)

textot Mar 13, 2021