Find the missing term or terms in each geometric sequence

15) ..., −3, ___, −108, ... 16) ..., −2, ___, −18, ...
17) ..., −3, ___, −75, ... 18) ..., 2, ___, 18, ...
asked Oct 29, 2018
reshown Oct 29, 2018

15)
The given Series
..., −3, ___, −108,....
Let the missing number be "x"
In GP common ratios are equal
Hence,
x / (-3)  =  (-108) / x
x^2  =  (-3)(-108)
x^2  =  324
Apply Square root on each side
x  =  √324
x  =  18

16)
The given Series
..., −2, ___, −18,....
Let the missing number be "x"
In GP common ratios are equal
Hence,
x / (-2)  =  (-18) / x
x^2  =  (-2)(-18)
x^2  =  36
Apply Square root on each side
x  =  √36
x  =  6

17)
The given Series
..., −3, ___, −75, ...
Let the missing number be "x"
In GP common ratios are equal
Hence,
x / (-3)  =  (-75) / x
x^2  =  (-3)(-75)
x^2  =  225
Apply Square root on each side
x  =  √225
x  =  15

18)
The given Series
..., 2, ___, 18,....
Let the missing number be "x"
In GP common ratios are equal
Hence,
x / (2)  =  (18) / x
x^2  =  (2)(18)
x^2  =  36
Apply Square root on each side
x  =  √36
x  =  6
answered Oct 30, 2018