11) The common ratio should be - 5. So, you would have the sequence of:
37, - 185, 925, - 4,625........etc.
12)
N=(L - F) / D + 1, where N=Number of terms, L=Last term, F=First term, D = Common difference
N=(65 - (-5)) / 5 +1
N = 15 - Number of terms
Sum = (F + L) / 2 x N
Sum = (-5 + 65) / 2 x 15
Sum = (60) / 2 x 15
Sum = 450
GP 37, ... 925
925/37=25
So the common ratio must be a factor of the form 25 to the power of some number
The obvious ones to try are \(\pm25\;\;or\;\; \pm5\)
-185/37 = -5 could be that one
-4625/37 = -125 = (-5)^3 or that one
-925/37 = -25 = (-5)^2 or that one, no that cannot work, just by inspection.
481/37 = 13 not that one
37, 37*-5, 37*-5*-5,.....
37, -185, 925, -4625,
so there are two answers and both have the common ratio of -5