Geometric Series

Whenever I think geometric series I think multiplication. So that means the first 1st times a number (lets just call it x) equals the 2nd number. And the 2nd term times this same number x equals the 3rd term, so on and so forth.

So you'll know that the number in inbetween 35 and 875, otherwise the multiplication doesnt work. This rules out b and c.

455 looks a little to big to be multiplied so d. Seems like the best answer.

Let's prove it though.

To find the number that needs to be multiplied between terms, divide our suspected answer -175 by the first term.

-175/35 = -5.

Ok great now lets multiply -175 by -5 and see if we get 875 (our 3rd term)

-175 x -5 = 875.

Boom! Nailed it!

Thanks for the question, let us know if it helped or not and I'm sure me or another member would be happy to help more if you need it. 

Thanks, Ninja   ....here's another approach

We have to multiply the first term by the constant ratio - call it, r -  twice to get to the third term....this means that :

875 / 35  = r^2

25  = r^2      take the positive/neg sq root of both sides

±5 = r

So, either r = 5 or r = -5.....

Then the second term is either   35 * 5  = 175

Or the second term is  35 * - 5  =  -175

And the second must be correct.....so.....the common ratio =  -5   and the answer is "d"