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

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,

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