Geometric sequence has U₃= 1458 and U₆= -432 find r..

Yeah, theyve made a (fairly obvious) mistake.
The sum to infinity with r=2/3 must be greater than the initial value, whereas the sum to infinity with r=-2/3 must be less than the initial value, just by a simple rough cancelling argument.

Yeah, a clear rookie mistake. Something I was doing when I first started and something that you’re consistently told to be by careful not to do.
Sorry, what do you mean with the sum to infinity part?

Assuing u1 is positive and r=-2/3 (for example), then
u2 + u3 < 0
u4 + u5 < 0
u6 + u7 < 0
....
So the sum to infinity (and 20 here is close to infinity) must be less than u1.
Conversely if r>0, then all the terms are positive and the sum to infinity is greater than u1.

I’ll see if I can make sense of what you’re explaining.
In the case r<0, in this case r=-2/3…
U₁ being positive, in this case 3280.5..
Every two consecutive terms added together < 0
Does the r<0 explain the oscillating reasoning?
The sum to infinity will be less than the first term?