Find the missing term or terms in each geometric sequence

Question

15) ..., −3, ___, −108, ... 16) ..., −2, ___, −18, ...

17) ..., −3, ___, −75, ... 18) ..., 2, ___, 18, ...

Answer 1

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