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Determine if the sequence is geometric. If it is, find the common ratio.

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Determine if the sequence is geometric. If it is, find the common ratio.

1) −1, 6, −36, 216, ... 2) −1, 1, 4, 8, ...
3) 4, 16, 36, 64, ... 4) −3, −15, −75, −375, 
asked Oct 23, 2018 in ALGEBRA 2 by anonymous

1 Answer

0 votes

1)

−1, 6, −36, 216, ... 

t1  =  -1

t2  =  6

t3  =  -36

r  =  t2 / t1           or          r  =  t3 / t2

   =  6/(-1)                            =  -36/6

   =  -6                                  =  -6    

Above Ratios are equal

Hence, Given Series is in GP

Common Ratio (r)  =  -6

 

2)

−1, 1, 4, 8, ...

t1  =  -1

t2  =  1

t3  =  4

r  =  t2 / t1           or          r  =  t3 / t2

   =  1/(-1)                            =  4/1

   =  -1                                 =  4    

Above Ratios are not equal

Hence, Given Series is not in GP

 

3) 4, 16, 36, 64, ...

t1  =  4

t2  =  16

t3  =  36

r  =  t2 / t1           or          r  =  t3 / t2

   =  16/4                            =  36/16

   =  4                                 =  9/4    

Above Ratios are not equal

Hence, Given Series is not in GP

 

4)
−3, −15, −75, −375, 

t1  =  -3

t2  =  -15

t3  =  -75

r  =  t2 / t1           or          r  =  t3 / t2

   =  (-15)/(-3)                      =  (-75)/(-15)

   =  5                                  =  5    

Above Ratios are equal

Hence, Given Series is in GP

Common Ratio (r)  =  5

answered Oct 24, 2018 by homeworkhelp Mentor
edited Oct 27, 2018 by bradely

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